Answer
Hypothesis testing of one sample proportion.
The null hypothesis for testing is defined as
\[{{H}_{0}}:p=0.42\]
that is, the people who prefer Pepsi.
The alternative hypothesis is defined as
\[{{H}_{1}}:p\ne 0.42\]
that is, the people who do not prefer Pepsi.
There are 53 out of 100 who prefer Pepsi. The p-value is calculated in Minitab and the steps are as follows:
Step 1: Go to Stats, then basic statistics, and then 1 sample proportion test.
Step 2: A new dialog box appears. Click on summarized data; enter 53 in place of number of events and 100 in the place of number of trials. Select perform hypothesis test and enter 0.42 in the place of hypothesized proportion.
Step 3: Go to options and set confidence level as 95% and alternative hypothesis as not equals to in two-tailed test. Choose “use test and interval based on normal distribution,” then ok.
The p-value is generated as 0.026, which is less than 0.05. So, the null hypothesis gets rejected and it conveys that people do not prefer Pepsi.
The null hypothesis for testing is defined as
\[{{H}_{0}}:p=0.43\], that is, the people who prefer Pepsi.
The alternative hypothesis is defined as
\[{{H}_{1}}:p\ne 0.43\], that is, the people who do not prefer Pepsi.
There are 53 out of 100 who prefer Pepsi. The p-value is calculated in Minitab and steps are as follows:
Step 1: Go to Stats, then basic statistics, and then 1 sample proportion test.
Step 2: A new dialog box appears. Click on summarized data; enter 53 in place of number of events and 100 in the place of number of trials. Select perform hypothesis test and enter 0.42 in the place of hypothesized proportion.
Step 3: Go to options and set confidence level as 95% and alternative hypothesis as not equals to in two-tailed test. Choose “use test and interval based on normal distribution,” then ok.
The p-value is generated as 0.043, which is less than 0.05. So, the null hypothesis gets rejected and it conveys that people do not prefer Pepsi.
The null hypothesis for testing is defined as
\[{{H}_{0}}:p=0.44\], that is, the people who prefer Pepsi.
The alternative hypothesis is defined as
\[{{H}_{1}}:p\ne 0.44\], that is the people who do not prefer Pepsi.
There are 53 out of 100 who prefer Pepsi. The p-value is calculated in Minitab and the steps are as follows:
Step 1: Go to Stats, then basic statistics, and then 1 sample proportion test.
Step 2: A new dialog box appears. Click on summarized data; enter 53 in place of number of events and 100 in the place of number of trials. Select perform hypothesis test and enter 0.44 in the place of hypothesized proportion.
Step 3: Go to options and set confidence level as 95% and alternative hypothesis as not equals to in two-tailed test. Choose “use test and interval based on normal distribution,” then ok.
The p-value is generated as 0.070, which is more than 0.05. So, the null hypothesis does not get rejected and it conveys that people prefer Pepsi.
The null hypothesis for testing is defined as
\[{{H}_{0}}:p=0.45\], that is, the people who prefer Pepsi.
The alternative hypothesis is defined as
\[{{H}_{1}}:p\ne 0.45\], that is, the people who do not prefer Pepsi.
There are 53 out of 100 who prefer Pepsi. The p-value is calculated in Minitab and the steps are as follows:
Step 1: Go to Stats, then basic statistics, and then 1 sample proportion test.
Step 2: A new dialog box appears. Click on summarized data; enter 53 in place of number of events and 100 in the place of number of trials. Select perform hypothesis test and enter 0.45 in the place of hypothesized proportion.
Step 3: Go to options and set confidence level as 95% and alternative hypothesis as not equals to in two-tailed test. Choose “use test and interval based on normal distribution,” then ok.
The p-value is generated as 0.108, which is more than 0.05. So, the null hypothesis does not get rejected and it conveys that people prefer Pepsi.
The null hypothesis for testing is defined as,
\[{{H}_{0}}:p=0.46\], that is, the people who prefer Pepsi.
The alternative hypothesis is defined as
\[{{H}_{1}}:p\ne 0.46\], that is, the people who do not prefer Pepsi.
There are 53 out of 100 who prefer Pepsi. The p-value is calculated in Minitab and steps are as follows:
Step 1: Go to Stats, then basic statistics, and then 1 sample proportion test.
Step 2: A new dialog box appears. Click on summarized data; enter 53 in place of number of events and 100 in the place of number of trials. Select perform hypothesis test and enter 0.46 in the place of hypothesized proportion.
Step 3: Go to options and set confidence level as 95% and alternative hypothesis as not equals to in two-tailed test. Choose “use test and interval based on normal distribution,” then ok.
The p-value is generated as 0.160, which is more than 0.05. So, the null hypothesis does not get rejected and it conveys that people prefer Pepsi.
The null hypothesis for testing is defined as
\[{{H}_{0}}:p=0.47\], that is, the people who prefer Pepsi.
The alternative hypothesis is defined as
\[{{H}_{1}}:p\ne 0.47\], that is, the people who do not prefer Pepsi.
There are 53 out of 100 who prefer Pepsi. The p-value is calculated in Minitab and the steps are as follows:
Step 1: Go to Stats, then basic statistics, and then1 sample proportion test.
Step 2: A new dialog box appears. Click on summarized data; enter 53 in place of number of events and 100 in the place of number of trials. Select perform hypothesis test and enter 0.47 in the place of hypothesized proportion.
Step 3: Go to options and set confidence level as 95% and alternative hypothesis as not equals to in two-tailed test. Choose “use test and interval based on normal distribution,” then ok.
The p-value is generated as 0.229, which is more than 0.05. So, the null hypothesis does not get rejected and it conveys that people prefer Pepsi.
The null hypothesis for testing is defined as
\[{{H}_{0}}:p=0.48\], that is, the people who prefer Pepsi.
The alternative hypothesis is defined as
\[{{H}_{1}}:p\ne 0.48\], that is, the people who do not prefer Pepsi.
There are 53 out of 100 who prefer Pepsi. The p-value is calculated in Minitab and steps are as follows:
Step 1: Go to Stats, then basic statistics, and then 1 sample proportion test.
Step 2: A new dialog box appears. Click on summarized data; enter 53 in place of number of events and 100 in the place of number of trials. Select perform hypothesis test and enter 0.48 in the place of hypothesized proportion.
Step 3: Go to options and set confidence level as 95% and alternative hypothesis as not equals to in two-tailed test. Choose “use test and interval based on normal distribution,” then ok.
The p-value is generated as 0.317, which is more than 0.05. So, the null hypothesis does not get rejected and it conveys that people prefer Pepsi.
The null hypothesis for testing is defined as
\[{{H}_{0}}:p=0.49\], that is, the people who prefer Pepsi.
The alternative hypothesis is defined as
\[{{H}_{1}}:p\ne 0.49\], that is the people who do not prefer Pepsi.
There are 53 out of 100 who prefer Pepsi. The p-value is calculated in Minitab and the steps are as follows:
Step 1: Go to Stats, then basic statistics, and then 1 sample proportion test.
Step 2: A new dialog box appears. Click on summarized data; enter 53 in place of number of events and 100 in the place of number of trials. Select perform hypothesis test and enter 0.49 in the place of hypothesized proportion.
Step 3: Go to options and set confidence level as 95% and alternative hypothesis as not equals to in two-tailed test. Choose “use test and interval based on normal distribution,” then ok.
The p-value is generated as 0.424, which is more than 0.05. So, the null hypothesis does not get rejected and it conveys that people prefer Pepsi.
The null hypothesis for testing is defined as
\[{{H}_{0}}:p=0.50\], that is, the people who prefer Pepsi.
The alternative hypothesis is defined as
\[{{H}_{1}}:p\ne 0.50\], that is the people who do not prefer Pepsi. There are 53 out of 100 who prefer Pepsi. The p-value is calculated in Minitab and the steps are as follows:
Step 1: Go to Stats, then basic statistics, and then 1 sample proportion test.
Step 2: A new dialog box appears. Click on summarized data; enter 53 in place of number of events and 100 in the place of number of trials. Select perform hypothesis test and enter 0.50 in the place of hypothesized proportion.
Step 3: Go to options and set confidence level as 95% and alternative hypothesis as not equals to in two-tailed test. Choose “use test and interval based on normal distribution,” then ok.
The p-value is generated as 0.549, which is more than 0.05. So, the null hypothesis does not get rejected and it conveys that people prefer Pepsi.
The null hypothesis for testing is defined as
\[{{H}_{0}}:p=0.51\], that is, the people who prefer Pepsi.
The alternative hypothesis is defined as
\[{{H}_{1}}:p\ne 0.51\], that is, the people who do not prefer Pepsi. There are 53 out of 100 who prefer Pepsi. The p-value is calculated in Minitab and the steps are as follows:
Step 1: Go to Stats, then basic statistics, and then 1 sample proportion test.
Step 2: A new dialog box appears. Click on summarized data; enter 53 in place of number of events and 100 in the place of number of trials. Select perform hypothesis test and enter 0.51 in the place of hypothesized proportion.
Step 3: Go to options and set confidence level as 95% and alternative hypothesis as not equals to in two-tailed test. Choose “use test and interval based on normal distribution,” then ok.
The p-value is generated as 0.689, which is more than 0.05. So, the null hypothesis does not get rejected and it conveys that people prefer Pepsi.
The null hypothesis for testing is defined as
\[{{H}_{0}}:p=0.52\], that is, the people who prefer Pepsi.
The alternative hypothesis is defined as
\[{{H}_{1}}:p\ne 0.52\], that is, the people who do not prefer Pepsi.
There are 53 out of 100 who prefer Pepsi. The p-value is calculated in Minitab and the steps are as follows:
Step 1: Go to Stats, then basic statistics, and then 1 sample proportion test.
Step 2: A new dialog box appears. Click on summarized data; enter 53 in place of number of events and 100 in the place of number of trials. Select perform hypothesis test and enter 0.52 in the place of hypothesized proportion.
Step 3: Go to options and set confidence level as 95% and alternative hypothesis as not equals to in two-tailed test. Choose “use test and interval based on normal distribution,” then ok.
The p-value is generated as 0.841, which is more than 0.05. So, the null hypothesis does not get rejected and it conveys that people prefer Pepsi.
The null hypothesis for testing is defined as
\[{{H}_{0}}:p=0.53\], that is, the people who prefer Pepsi.
The alternative hypothesis is defined as
\[{{H}_{1}}:p\ne 0.53\], that is the people who do not prefer Pepsi. There are 53 out of 100 who prefer Pepsi. The p-value is calculated in Minitab and the steps are as follows:
Step 1: Go to Stats, then basic statistics, and then 1 sample proportion test.
Step 2: A new dialog box appears. Click on summarized data; enter 53 in place of number of events and 100 in the place of number of trials. Select perform hypothesis test and enter 0.53 in the place of hypothesized proportion.
Step 3: Go to options and set confidence level as 95% and alternative hypothesis as not equals to in two-tailed test. Choose “use test and interval based on normal distribution,” then ok.
The p-value is generated as 1.000, which is more than 0.05. So, the null hypothesis does not get rejected and it conveys that people prefer Pepsi.
The null hypothesis for testing is defined as
\[{{H}_{0}}:p=0.54\], that is, the people who prefer Pepsi.
The alternative hypothesis is defined as
\[{{H}_{1}}:p\ne 0.54\], that is the people who do not prefer Pepsi.
There are 53 out of 100 who prefer Pepsi. The p-value is calculated in Minitab and the steps are as follows:
Step 1: Go to Stats, then basic statistics, and then 1 sample proportion test.
Step 2: A new dialog box appears. Click on summarized data; enter 53 in place of number of events and 100 in the place of number of trials. Select perform hypothesis test and enter 0.54 in the place of hypothesized proportion.
Step 3: Go to options and set confidence level as 95% and alternative hypothesis as not equals to in two-tailed test. Choose “use test and interval based on normal distribution,” then ok.
The p-value is generated as 0.841, which is more than 0.05. So, the null hypothesis does not get rejected and it conveys that people prefer Pepsi.
The null hypothesis for testing is defined as
\[{{H}_{0}}:p=0.55\], that is, the people who prefer Pepsi.
The alternative hypothesis is defined as
\[{{H}_{1}}:p\ne 0.55\], that is the people who do not prefer Pepsi.
There are 53 out of 100 who prefer Pepsi. The p-value is calculated in Minitab and the steps are as follows:
Step 1: Go to Stats, then basic statistics, and then 1 sample proportion test.
Step 2: A new dialog box appears. Click on summarized data; enter 53 in place of number of events and 100 in the place of number of trials. Select perform hypothesis test and enter 0.55 in the place of hypothesized proportion.
Step 3: Go to options and set confidence level as 95% and alternative hypothesis as not equals to in two-tailed test. Choose “use test and interval based on normal distribution” then ok.
The p-value is generated as 0.688, which is more than 0.05. So the null hypothesis does not get rejected and it conveys that people prefer Pepsi.
The null hypothesis for testing is defined as
\[{{H}_{0}}:p=0.56\], that is the people who prefer Pepsi.
The alternative hypothesis is defined as
\[{{H}_{1}}:p\ne 0.56\], that is the people who do not prefer Pepsi.
There are 53 out of 100 who prefer Pepsi. The p-value is calculated in Minitab and the steps are as follows:
Step 1: Go to Stats, then basic statistics, and then 1 sample proportion test.
Step 2: A new dialog box appears. Click on summarized data; enter 53 in place of number of events and 100 in the place of number of trials. Select perform hypothesis test and enter 0.56 in the place of hypothesized proportion.
Step 3: Go to options and set confidence level as 95% and alternative hypothesis as not equals to in two-tailed test. Choose “use test and interval based on normal distribution,” then ok.
The p-value is generated as 0.546, which is more than 0.05. So, the null hypothesis does not get rejected and it conveys that people prefer Pepsi.
The null hypothesis for testing is defined as
\[{{H}_{0}}:p=0.57\], that is, the people who prefer Pepsi.
The alternative hypothesis is defined as
\[{{H}_{1}}:p\ne 0.57\], that is, the people who do not prefer Pepsi. There are 53 out of 100 who prefer Pepsi. The p-value is calculated in Minitab and the steps are as follows:
Step 1: Go to Stats, then basic statistics, and then 1 sample proportion test.
Step 2: A new dialog box appears. Click on summarized data; enter 53 in place of number of events and 100 in the place of number of trials. Select perform hypothesis test and enter 0.57 in the place of hypothesized proportion.
Step 3: Go to options and set confidence level as 95% and alternative hypothesis as not equals to in two-tailed test. Choose “use test and interval based on normal distribution” then ok.
The p-value is generated as 0.419, which is more than 0.05. So, the null hypothesis does not get rejected and it conveys that people prefer Pepsi.
The null hypothesis for testing is defined as
\[{{H}_{0}}:p=0.58\], that is, the people who prefer Pepsi.
The alternative hypothesis is defined as
\[{{H}_{1}}:p\ne 0.58\], that is, the people who do not prefer Pepsi.
There are 53 out of 100 who prefer Pepsi. The p-value is calculated in Minitab and the steps are as follows:
Step 1: Go to Stats, then basic statistics, and then 1 sample proportion test.
Step 2: A new dialog box appears. Click on summarized data; enter 53 in place of number of events and 100 in the place of number of trials. Select perform hypothesis test and enter 0.58 in the place of hypothesized proportion.
Step 3: Go to options and set confidence level as 95% and alternative hypothesis as not equals to in two-tailed test. Choose “use test and interval based on normal distribution,” then ok.
The p-value is generated as 0.311, which is more than 0.05. So the null hypothesis does not get rejected and it conveys that people prefer Pepsi.
The null hypothesis for testing is defined as
\[{{H}_{0}}:p=0.59\], that is, the people who prefer Pepsi.
The alternative hypothesis is defined as
\[{{H}_{1}}:p\ne 0.59\], that is the people who do not prefer Pepsi.
There are 53 out of 100 who prefer Pepsi. The p-value is calculated in Minitab and the steps are as follows:
Step 1: Go to Stats, then basic statistics, and then 1 sample proportion test.
Step 2: A new dialog box appears. Click on summarized data; enter 53 in place of number of events and 100 in the place of number of trials. Select perform hypothesis test and enter 0.59 in the place of hypothesized proportion.
Step 3: Go to options and set confidence level as 95% and alternative hypothesis as not equals to in two-tailed test. Choose “use test and interval based on normal distribution,” then ok.
The p-value is generated as 0.222, which is more than 0.05. So, the null hypothesis does not get rejected and it conveys that people prefer Pepsi.
The null hypothesis for testing is defined as
\[{{H}_{0}}:p=0.60\], that is the people who prefer Pepsi.
The alternative hypothesis is defined as
\[{{H}_{1}}:p\ne 0.60\], that is, the people who do not prefer Pepsi.
There are 53 out of 100 who prefer Pepsi. The p-value is calculated in Minitab and steps are as follows:
Step 1: Go to Stats, then basic statistics, and then 1 sample proportion test.
Step 2: A new dialog box appears. Click on summarized data; enter 53 in place of number of events and 100 in the place of number of trials. Select perform hypothesis test and enter 0.60 in the place of hypothesized proportion.
Step 3: Go to options and set confidence level as 95% and alternative hypothesis as not equals to in two-tailed test. Choose “use test and interval based on normal distribution,” then ok.
The p-value is generated as 0.153, which is more than 0.05. So, the null hypothesis does not get rejected and it conveys that people prefer Pepsi.
The null hypothesis for testing is defined as
\[{{H}_{0}}:p=0.61\], that is the people who prefer Pepsi.
The alternative hypothesis is defined as
\[{{H}_{1}}:p\ne 0.61\], that is the people who do not prefer Pepsi.
There are 53 out of 100 who prefer Pepsi. The p-value is calculated in Minitab and the steps are as follows:
Step 1: Go to Stats, then basic statistics, and then 1 sample proportion test.
Step 2: A new dialog box appears. Click on summarized data; enter 53 in place of number of events and 100 in the place of number of trials. Select perform hypothesis test and enter 0.61 in the place of hypothesized proportion.
Step 3: Go to options and set confidence level as 95% and alternative hypothesis as not equals to in two-tailed test. Choose “use test and interval based on normal distribution,” then ok.
The p-value is generated as 0.101, which is more than 0.05. So, the null hypothesis does not get rejected and it conveys that people prefer Pepsi.
The null hypothesis for testing is defined as
\[{{H}_{0}}:p=0.62\], that is, the people who prefer Pepsi.
The alternative hypothesis is defined as
\[{{H}_{1}}:p\ne 0.62\], that is, the people who do not prefer Pepsi.
There are 53 out of 100 who prefer Pepsi. The p-value is calculated in Minitab and the steps are as follows:
Step 1: Go to Stats, then basic statistics, and then 1 sample proportion test.
Step 2: A new dialog box appears. Click on summarized data; enter 53 in place of number of events and 100 in the place of number of trials. Select perform hypothesis test and enter 0.62 in the place of hypothesized proportion.
Step 3: Go to options and set confidence level as 95% and alternative hypothesis as not equals to in two-tailed test. Choose “use test and interval based on normal distribution,” then ok.
The p-value is generated as 0.0654, which is more than 0.05. So, the null hypothesis does not get rejected and it conveys that people prefer Pepsi.
The null hypothesis for testing is defined as
\[{{H}_{0}}:p=0.63\], that is, the people who prefer Pepsi.
The alternative hypothesis is defined as
\[{{H}_{1}}:p\ne 0.63\], that is, the people who do not prefer Pepsi.
There are 53 out of 100 who prefer Pepsi. The p-value is calculated in Minitab and thersteps are as follows:
Step 1: Go to Stats, then basic statistics, and then 1 sample proportion test.
Step 2: A new dialog box appears. Click on summarized data; enter 53 in place of number of events and 100 in the place of number of trials. Select perform hypothesis test and enter 0.63 in the place of hypothesized proportion.
Step 3: Go to options and set confidence level as 95% and alternative hypothesis as not equals to in two-tailed test. Choose “use test and interval based on normal distribution,” then ok.
The p-value is generated as 0.038, which is less than 0.05. So, the null hypothesis gets rejected and it conveys that people do not prefer Pepsi.
The null hypothesis for testing is defined as
\[{{H}_{0}}:p=0.64\], that is the people who prefer Pepsi.
The alternative hypothesis is defined as
\[{{H}_{1}}:p\ne 0.64\], that is the people who do not prefer Pepsi.
There are 53 out of 100 who prefer Pepsi. The p-value is calculated in Minitab and the steps are as follows:
Step 1: Go to Stats, then basic statistics, and then 1 sample proportion test.
Step 2: A new dialog box appears. Click on summarized data; enter 53 in place of number of events and 100 in the place of number of trials. Select perform hypothesis test and enter 0.64 in the place of hypothesized proportion.
Step 3: Go to options and set confidence level as 95% and alternative hypothesis as not equals to in two-tailed test. Choose “use test and interval based on normal distribution,” then ok.
The p-value is generated as 0.022, which is less than 0.05. So, the null hypothesis gets rejected and it conveys that people do not prefer Pepsi.
Work Step by Step
Given above.
