Question

The National Sleep Foundation surveyed representative samples of adults in six different countries to ask questions about sleeping habits.† Each person in a representative sample of 250 adults in each of these countries was asked how much sleep they get on a typical work night. For the United States, the sample mean was 391 minutes, and for Mexico the sample mean was 426 minutes. Suppose that the sample standard deviations were 27 minutes for the U.S. sample and 42 minutes for the Mexico sample. The report concludes that on average, adults in the United States get less sleep on work nights than adults in Mexico. Is this a reasonable conclusion? Support your answer with an appropriate hypothesis test. (Use α = 0.05. Use μ1 for Mexico and μ2 for the United States.)

State the appropriate null and alternative hypotheses.

H0: μ1 − μ2 = 0 Ha: μ1 − μ2 > 0

H0: μ1 − μ2 < 0 Ha: μ1 − μ2 > 0

H0: μ1 − μ2 ≠ 0 Ha: μ1 − μ2 = 0

H0: μ1 − μ2 > 0 Ha: μ1 − μ2 = 0

H0: μ1 − μ2 = 0 Ha: μ1 − μ2 ≠ 0

Find the test statistic and P-value. (Use a table or technology. Round your test statistic to one decimal place and your P-value to three decimal places.)

t =

P-value =

State the conclusion in the problem context.

We fail to reject H0. It is reasonable to conclude that on average, adults in the United States get less sleep on work nights than adults in Mexico.

We reject H0. It is reasonable to conclude that on average, adults in the United States get less sleep on work nights than adults in Mexico.

We reject H0. It is not reasonable to conclude that on average, adults in the United States get less sleep on work nights than adults in Mexico.

We fail to reject H0. It is not reasonable to conclude that on average, adults in the United States get less sleep on work nights than adults in Mexico.

Answer #1

H0: μ1 − μ2 = 0

Ha: μ1 − μ2 > 0

Test Statistic :-

t = 11.0835 11.1

Test Criteria :-

Reject null hypothesis if

DF = 424

Result :- Reject Null Hypothesis

Decision based on P value

P - value = P ( t > 11.0835 ) = 0

Reject null hypothesis if P value <
level of significance

P - value = 0 < 0.05 ,hence we reject null hypothesis

Conclusion :- Reject null hypothesis

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