Question

Can you conclude with a high degree of confidence that the population means for Iowa and New Jersey students are​ different? A. Because of the extremely low p​-value, we cannot reject the null hypothesis with a very high degree of confidence.​ Hence, the population means for Iowa and New Jersey students are not different. B. Because of the extremely high p​-value, we can reject the null hypothesis with a very high degree of confidence.​ Hence, the population means for Iowa and New Jersey students are different. C. Because of the extremely low p​-value, we can reject the null hypothesis with a very high degree of confidence.​ Hence, the population means for Iowa and New Jersey students are different. D. Because of the extremely high p​-value, we cannot reject the null hypothesis with a very high degree of confidence.​ Hence, the population means for Iowa and New Jersey students are not different.

Answer 1

Complete Question

The complete question is shown on the first uploaded image

Answer:

Option A is correct

Explanation:

From the question we are told that

The 95% confidence interval of the mean score of all New Jersey third graders is (58.957 , 63.043)

The sample size is n = 184

The sample average is
`\mu = 65 \ points`

The standard deviation is
`\sigma  =  13 \ points`

The 90% confidence interval for the difference in mean score between lowa and New Jersey is (-6.33 , -1.67 )

The p-value is
`p-value  =  0.0048`

Generally given that the p-values is very low compared to the level of significance (100 -90 = 10% = 0.10 ) we can reject the null hypothesis which is usually a claim that the means of the population are the same )

Hence the population means are different .