According to the report the standard deviation of monthly ce

According to the report, the standard deviation of monthly cell phone bills was $48.65 three years ago. A researcher suspects that the standard deviation of monthly cell phone bills is higher today.

(a) Determine the null and alternative hypothesis. Choose the correct answer below.

a. H0: ? =$48.65; H₁ : ? > $48.65

b. H0: ? =$48.65; H₁ : ? > $48.65

c. H0: ? =$48.65; H₁ : ? < $48.65

d. H0: ? =$48.65; H₁ : ? ? $48.65

(b) Explain what it would mean to make a Type I error. Choose the correct answer below.

a. The sample evidence did not lead the researcher to believe the standard deviation of monthly cell phone bills is higher than $48.65, when in fact the standard deviation of bills is higher than $48.65.

b. The sample evidence led the researcher to believe the standard deviation of monthly cell phone bills is higher than $48.65, when in fact the standard deviation of bills is $48.65

c. The sample evidence led the researcher to believe the standard deviation of monthly cell phone bills is less than $48.65, when in fact the standard deviation of bills is $48.65.

(c) Explain what it would mean to make a Type II error. Choose the correct answer below.

a. The sample evidence did not lead the researcher to believe the standard deviation of monthly bills is less than $48.65, when in fact the standard deviation of bills is less than $48.65

b. The sample evidence did not lead the researcher to believe the standard deviation of monthly bills is higher than $48.65, when in fact the standard deviation of bills is higher than $48.56

c. The sample evidence led the researcher to believe the standard deviation of monthly bills is higher than $48.65, when in fact the standard deviation of bills is higher than $48.56

Solution

(a) a. H0: ? =$48.65; H₁ : ? > $48.65

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(b) Type I error: We reject the null hypothesis when it is true.

Answer: b. The sample evidence led the researcher to believe the standard deviation of monthly cell phone bills is higher than $48.65, when in fact the standard deviation of bills is $48.65

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(c) Type II error: We do not reject the null hypothesis when it is false.

Answer: b. The sample evidence did not lead the researcher to believe the standard deviation of monthly bills is higher than $48.65, when in fact the standard deviation of bills is higher than $48.56