Question

Dr. Marcel grows two varieties of roses: damamask and cabbage. She took a sample of each variety to test if the average caloric contents were significantly different. Dr. Marcel wants to use these results to test H₀: µ_Damamask=µ_Cabbage versus H₀: µ_Damamask≠µ_Cabbage.

Based on her data, she found that the 95% confidence interval for µ_Damamask-µ_Cabbage is 4 +/- 3.60 and the   99% confidence interval for µ_Damamask-µ_Cabbage is 4 +/- 4.74. Based on the interval, what do we know about the corresponding p-value and conclusions?

	a.	The p-value is between 0.01 and 0.05, and thus we will reject the null hypothesis at the 5% significance level, but not at the 1% significance level.
	b.	The p-value is less than 0.01 and thus we will reject the null hypothesis at the 1% significance level.
	c.	More information is needed to determine the p-value and the corresponding conclusions about the hypothesis tests.
	d.	The p-value is larger than 0.05, and thus we will not reject the null hypothesis at the 5% significance level.

Answer 1

if we look at the interval closely

95% confidence interval for µ_Damamask-µ_Cabbage is 4 +/- 3.60

hence it does not contain a 0

Means the null hypothesis is rejected and p value is less than 0.05

99% confidence interval for µ_Damamask-µ_Cabbage is 4 +/- 4.74

hence it contains a 0

Means the null hypothesis is not rejected and p value is greater than 0.01

hence,

A) The p-value is between 0.01 and 0.05, and thus we will reject the null hypothesis at the 5% significance level, but not at the 1% significance level.

answered by: anonymous