According to the Centers for Disease Control and Prevention (February 18, 2016), 1 in 3 American adults don’t get enough sleep. A researcher wants to determine if Americans are sleeping less than the recommended 7 hours of sleep on weekdays. He takes a random sample of 150 Americans and computes the average sleep time of 6.7 hours on weekdays. Assume that the population is normally distributed with a known standard deviation of 2.1 hours. Test the researcher’s claim at α = 0.01. (You may find it useful to reference the appropriate table:z table or t table) a. Select the relevant null and the alternative hypotheses.
H0: μ = 7; HA: μ ≠ 7
H0: μ ≤ 7; HA: μ ≥ 7
H0: μ ≥ 7; HA: μ < 7
b. Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)
Test statistic = ?
c. Find the p-value.
p-value < 0.01
0.01 ≤ p-value < 0.025
0.025 ≤ p-value < 0.05
0.05 ≤ p-value < 0.10
p-value ≥ 0.10
d. What is the conclusion at α = 0.01?
Reject H0 since the p-value is greater than α.
Reject H0 since the p-value is smaller than α.
Do not reject H0 since the p-value is greater than α.
Do not reject H0 since the p-value is smaller than α.
e. Make an inference.
There is insufficient evidence to suggest that Americans sleep less than the recommended 7 hours of sleep.
There is sufficient evidence to suggest that Americans sleep less than the recommended 7 hours of sleep.