Question

Data from an SRS of married couples was used to test the claim that spouses are not the same age, on average. The data was used to construct three different confidence intervals for the population mean difference in age, Ud:

90% confidence interval for Ud: (0.135, 4.265)
95% confidence interval for Ud : (-0.435, 4.835)
99% confidence interval for Ud: (-1.933, 6.333)

If we use the same data to test H0:Ud=0 versus H0=Ud≠0, what is the range for the p-value ?

	a.	There is not enough information to answer this question.
	b.	p-value > 0.10
	c.	0.01 < p-value < 0.05
	d.	0.05 < p-value < 0.10
	e.	p-value < 0.01

Answer 1

If we see the confidence intervals for 90% , 95% and 99% , i.e , levels of significance 0.10 , 0.05 and 0.01 , we see that 0 is not included only in the interval for alpha = 0.10. Therefore, the null hypothesis Ud = 0 is rejected only for alpha = 0.10. We know that, we reject the null hypothesis when p value<alpha. So, p value < 0.10.

For the confidence intervals at alpha = 0.05 and 0.01, zero is included in the interval. Therefore, the null hypothesis Ud = 0 is accepted at alpha = 0.01 and alpha 0.05.We know that, we accept the null hypothesis when p value>alpha. So, p value > 0.01>0.05.

Therefore, the correct range of the p value is:

d. 0.05<p-value<0.10