Question

According to a report, the standard deviation of monthly cell phone bills was $4.96 in 2017. A researcher suspects that the standard deviation 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 Il error.

Answer 1

The null hypothesis is that the standard deviation of monthly cell phone bills is still $4.96, while the alternative hypothesis is that it has changed. A Type I error means rejecting the null hypothesis when it is true, and a Type II error means failing to reject the null when the alternative is true.

Step-by-step explanation:

To answer the question about hypothesis testing regarding the belief that the standard deviation of monthly cell phone bills is different today (from 2017, when it was $4.96):

(a) Null and Alternative Hypotheses in Words

Null Hypothesis (H0): The standard deviation of monthly cell phone bills today is still $4.96.

Alternative Hypothesis (Ha): The standard deviation of monthly cell phone bills today is not $4.96.

(b) Null and Alternative Hypotheses Symbolically

H0: σ = $4.96

Ha: σ ≠ $4.96

(c) Explanation of a Type I Error

A Type I error occurs if we reject the null hypothesis when, in fact, it is true.

(d) Explanation of a Type II Error

A Type II error occurs if we fail to reject the null hypothesis when the alternative hypothesis is actually true.