Answer
a. $H_{o}: μ = 47.47$
$H_{1}: μ \ne 47.47$
b. Type-I Error: Sample evidence leads the researcher to believe that the mean monthly cell phone bill is not equal to 47.47 today. However, in fact the mean monthly bill is 47.47.
c. Type-II Error: Sample evidence leads the researcher to believe that the mean monthly cell phone bill is equal to 47.47 today. However, in fact the mean monthly bill is different from 47.47.
Work Step by Step
a. Null hypothesis (mean monthly cell phone bill is $\$47.47$):
$H_{o}: μ = 47.47$
Alternative hypothesis ( mean monthly cell phone bill is not $\$47.47$)
$H_{1}: μ \ne 47.47$
b. Type-I Error: Sample evidence leads the researcher to believe that the mean monthly cell phone bill is not equal to 47.47 today. However, in fact the mean monthly bill is 47.47. In other words, the researcher has rejected the null hypothesis ($H_o$), but it in fact is true.
c. Type-II Error: Sample evidence leads the researcher to believe that the mean monthly cell phone bill is equal to 47.47 today. However, in fact the mean monthly bill is different from 47.47. In other words, the researcher has not rejected the null hypothesis ($H_o$), when in fact the alternative hypothesis ($H_1$) is true.
