Some research has indicated that as people age they need less sleep. A random sample of adults was selected and the number of hours that they slept last night was recorded. Simple regression analysis was performed on this sample and the results are attached below. Which of the following statements is true using α=0.10? a. Because the 90% confidence interval for the population slope does not include zero, we fail to reject the null hypothesis and conclude that there is no relationship between the hours of sleep and the age of the adult.
b. Because the 90% confidence interval for the population slope includes zero, we can reject the null hypothesis and conclude that there is a relationship between the hours of sleep and the age of the adult.
c. Because the 90% confidence interval for the population slope includes zero, we fail to reject the null hypothesis and conclude that there is no relationship between the hours of sleep and the age of the adult.
d. Because the 90% confidence interval for the population slope does not include zero, we can reject the null hypothesis and conclude that there is a relationship between the hours of sleep and the age of the adult.

regression results, SUMMARY OUTPUT:

Regression Statistics:

Multiple-R 0.390730855
R-Square 0.152670601
Adjusted-R-Square 0.112321582
Standard-Error 0.8419499
Observations 23

df SS MS F significance-F
Regression 1 2.68222332 2.682223 3.78375 0.06526371
Residual 21 14.88647233 0.70888
Total 22 17.56869565

Coefficients Standard-Error t-stat P-value Lower-90.0% Upper-90.0%
Intercept 8.7660 0.659009748 13.30179 1.07E-11 7.632021559 9.899994251
Age 0.0257 0.013233234 1.94519 0.065264 -0.048512101 -0.002970113