Question

(Answers are given but could you please work through the problem and show me the steps?)

Chapter 9

Understand the difference between type I and type II errors.

Establish null and alternative hypotheses

The average U.S. daily internet use at home is two hours and twenty minutes. A sample of 64 homes in Soddy-Daisy showed an average usage of two hours and 50 minutes with a standard deviation of 80 minutes. We are interested in determining whether or not the average usage in Soddy-Daisy is significantly different from the U.S. average.

a.	State the null and alternative hypotheses to be tested.
b.	Compute the test statistic. (sample standard deviation is given)
c.	The null hypothesis is to be tested using α = .05. Determine the critical value(s) for this test.
d.	What do you conclude?

ANSWER:

a. H0: μ = 140 minutes Ha: μ ≠ 140 minutes b. Test statistic t = 3 c. t.025 = 1.998 and -t.025 = -1.998 d. Reject H0 and conclude that the average usage in Soddy-Daisy is significantly different from the national average of 140 minutes.

The Bureau of Labor Statistics reported that the average yearly income of dentists in the year 2012 was $110,000. A sample of 81 dentists, which was taken in 2013, showed an average yearly income of $120,000. Assume the standard deviation of the population of dentists’s incomes in 2012 is $36,000.

a.	We want to test and determine if there has been a significant increase in the average yearly income of dentists. Provide the null and the alternative hypotheses.
b.	Compute the test statistic.
c.	Determine the p-value; and at a 5% level of significance, test the hypotheses.

ANSWER:

a. H0: μ ≤ $110,000 Ha: μ > $110,000 b. z = 2.5 c. p-value = .0062 Since the p-value = .0062 < .05, reject H0. Therefore, it can be concluded that there has been a significant increase.

Answer 1