Question

according to a report, the mean of monthly cell phone bills was $49.32 in 2017. a researcher suspects that the mean of monthly cell phone bills is different today. (a) state the null and alternative hypotheses in words. (b) state the null and alternative hypotheses symbolically. (c) explain what it would mean to make a type i error. (d) explain what it would mean to make a type ii error. (b) state the hypotheses symbolically. ( h_0: mu=$ 49.32 ) ( h_1: mu
eq $ 49.32 ) (type integers or decimals. do not round.) (c) what would it mean to make a type i error? a. the sample evidence did not lead the researcher to believe the mean of monthly cell phone bills is higher than $49.32 when, in fact, the mean of bills is higher than $49.32. b. the sample evidence led the researcher to believe the mean of monthly cell phone bills is different from $49.32 when, in fact, the mean of bills is $49.32. c. the sample evidence did not lead the researcher to believe the mean of monthly cell phone bills is different from $49.32 when, in fact, the mean of bills is different from $49.32. d. the sample evidence led the researcher to believe the mean of monthly cell phone bills is higher than $49.32 when, in fact, the mean of bills is $49.32.

Explanation:

A Type I error occurs when the null hypothesis (\(H_0\)) is true, but we reject it. In this context, the null hypothesis \(H_0:\mu = 49.32\) (the mean monthly cell - phone bill is \(\$49.32\)). If we make a Type I error, it means we wrongly reject \(H_0\). That is, the sample evidence leads us to believe the mean is different from \(\$49.32\) (reject \(H_0\)) when in fact the mean is \(\$49.32\) (\(H_0\) is true).

Answer:

B. The sample evidence led the researcher to believe the mean of monthly cell phone bills is different from \(\$49.32\) when, in fact, the mean of bills is \(\$49.32\)