Question

In: Statistics and Probability

You may need to use the appropriate appendix table or technology to answer this question. A...

You may need to use the appropriate appendix table or technology to answer this question.

A report states that adults 18- to 24- years-old send and receive 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 from the mean for 18- to 24- year-olds.

(a)

State the null and alternative hypotheses we should use to test whether the population mean daily number of texts for 25- to 34-year-olds differs from the population daily mean number of texts for 18- to 24-year-olds. (Enter != for ≠ as needed.)

H0:

Ha:

(b)

Suppose a sample of thirty 25- to 34-year-olds showed a sample mean of 118.4 texts per day. Assume a population standard deviation of 33.17 texts per day.

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

p-value =

(c)

With

α = 0.05

as the level of significance, what is your conclusion?

Reject H0. We cannot conclude that the population mean daily texts for 25- to 34-year-olds differs significantly from the population mean of 128 daily texts for 18- 24-year-olds.Do not reject H0. We can conclude that the population mean daily texts for 25- to 34-year-olds differs significantly from the population mean of 128 daily texts for 18- 24-year-olds.    Do not reject H0. We cannot conclude that the population mean daily texts for 25- to 34-year-olds differs significantly from the population mean of 128 daily texts for 18- 24-year-olds.Reject H0. We can conclude that the population mean daily texts for 25- to 34-year-olds differs significantly from the population mean of 128 daily texts for 18- 24-year-olds.

(d)

Repeat the preceding hypothesis test using the critical value approach.

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

H0:

Ha:

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

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

test statistic≤test statistic≥

State your conclusion.

Reject H0. We cannot conclude that the population mean daily texts for 25- to 34-year-olds differs significantly from the population mean of 128 daily texts for 18- 24-year-olds.Do not reject H0. We can conclude that the population mean daily texts for 25- to 34-year-olds differs significantly from the population mean of 128 daily texts for 18- 24-year-olds.    Do not reject H0. We cannot conclude that the population mean daily texts for 25- to 34-year-olds differs significantly from the population mean of 128 daily texts for 18- 24-year-olds.Reject H0. We can conclude that the population mean daily texts for 25- to 34-year-olds differs significantly from the population mean of 128 daily texts for 18- 24-year-olds.

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Expert Solution

orchestra answered 2 years ago
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