Question-65

Suppose a \(95\%\) confidence interval for the mean weight of apples from a certain orchard is calculated to be\((150g, 170g)\). Which of the following statements are correct \(?\) (Select all that apply)

• If we were to test the null hypothesis \(H_0 : \mu = 165\) grams at the \(5\%\) level of significance, we would fail to reject \(H_0\).

• The interval suggests that the population mean could be as low as \(150g\) or as high as \(170g\).

• If we were to test the null hypothesis \(H_0 : \mu = 145\) grams at the \(5\%\) level of significance, we would reject \(H_0\).

• None of the above.

Hint

Answer

• If we were to test the null hypothesis \(H_0 : \mu = 165\) grams at the \(5\%\) level of significance, we would fail to reject \(H_0\).

• The interval suggests that the population mean could be as low as \(150g\) or as high as \(170g\).

• If we were to test the null hypothesis \(H_0 : \mu = 145\) grams at the \(5\%\) level of significance, we would reject \(H_0\).

• None of the above.

Solution

Option \(A\) is correct : Since \(165g\) is within the confidence interval, we fail to reject the null hypothesis that the population mean is \(165g\) at a \(5\%\) significance level.

Option \(B\) is correct : The confidence interval suggests that the population mean could reasonably be any value between \(150g\) and \(170g\).

Option \(C\) is correct : Since \(145g\) is outside the confidence interval, we would reject the null hypothesis that the population mean is \(145g\) at the \(5\%\) significance level.