Question

textRequest reports that adults 18–24 years old send and receive 128 texts every day. Suppose we take a sample of 25–34 year olds to see if their mean number of daily texts differs from the mean for 18–24 year olds reported by TextRequest.

a. State the null and alternative hypotheses we should use to test whether the popu-lation mean daily number of texts for 25–34 year olds differs from the population daily mean number of texts for 18–24 year olds.

b. Suppose a sample of thirty 25–34 year olds showed a sample mean of 118.6 texts per day. Assume a population standard deviation of 33.17 texts per day and com-pute the p-value.

c. With a = .05 as the level of significance, what is your conclusion? d. Repeat the preceding hypothesis test using the critical value approach.

d. Repeat the preceding hypothesis test using the critical value approach.

Answer 1

a)

The Null and Alternative Hypotheses are,

b)

Since the population standard deviation is known, the z statistic is used to test the hypothesis. The z statistic is obtained using the formula,

The p-value is obtained from z distribution table for z = -1.552

c)

P-value approach

Since the P-value is greater than significance level = 0.05 at 5% significance level, it can be concluded that the null hypothesis is not rejected.

d)

Critical-value approach

The z critical value is obtained from z distribution table for significance level = 0.05

Since the z statistic value is less than z critical at 5% significance level, it can be concluded that the null hypothesis is not rejected.