A report states that adults 18- to 24- years-old send andreceive 128 texts every day. Suppose we take a sample of 25- to 34-year-olds to see if their mean number of daily texts differs fromthe mean for 18- to 24- year-olds.

(a)

State the null and alternative hypotheses we should use to testwhether the population mean daily number of texts for 25- to34-year-olds differs from the population daily mean number of textsfor 18- to 24-year-olds. (Enter != for ≠ as needed.)

H₀:

  

H_a:

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(b)

Suppose a sample of thirty 25- to 34-year-olds showed a samplemean of 118.7 texts per day. Assume a population standard deviationof 33.17 texts per day.

Compute the p-value. (Round your answer to four decimalplaces.)

p-value =

(c)

With

α = 0.05

as the level of significance, what is your conclusion?

Reject H₀. We cannot conclude that thepopulation mean daily texts for 25- to 34-year-olds differssignificantly from the population mean of 128 daily texts for 18-24-year-olds.Do not reject H₀. We cannotconclude that the population mean daily texts for 25- to34-year-olds differs significantly from the population mean of 128daily texts for 18-24-year-olds.     RejectH₀. We can conclude that the population meandaily texts for 25- to 34-year-olds differs significantly from thepopulation mean of 128 daily texts for 18- 24-year-olds.Do notreject H₀. We can conclude that the populationmean daily texts for 25- to 34-year-olds differs significantly fromthe population mean of 128 daily texts for 18- 24-year-olds.

(d)

Repeat the preceding hypothesis test using the critical valueapproach.

State the null and alternative hypotheses. (Enter != for ≠ asneeded.)

H₀:

128

  

H_a:

   

Find the value of the test statistic. (Round your answer to twodecimal places.)

State the critical values for the rejection rule. (Useα = 0.05. Round your answer to two decimal places. If thetest is one-tailed, enter NONE for the unused tail.)

test statistic ≤ test statistic ≥

State your conclusion.

Reject H₀. We cannot conclude that thepopulation mean daily texts for 25- to 34-year-olds differssignificantly from the population mean of 128 daily texts for 18-24-year-olds.Do not reject H₀. We cannotconclude that the population mean daily texts for 25- to34-year-olds differs significantly from the population mean of 128daily texts for 18-24-year-olds.     RejectH₀. We can conclude that the population meandaily texts for 25- to 34-year-olds differs significantly from thepopulation mean of 128 daily texts for 18- 24-year-olds.Do notreject H₀. We can conclude that the populationmean daily texts for 25- to 34-year-olds differs significantly fromthe population mean of 128 daily texts for 18- 24-year-olds.