True or False Justify for full credit a A 95 confidence inte

True or False. Justify for full credit.

(a) A 95% confidence interval is wider than a 90% confidence interval of the same parameter.

(b) In a right-tailed test, the value of the test statistic is 1.5. If we know the test statistic follows a Student’s t-distribution with P(T < 1.5) = 0.96, then we fail to reject the null hypothesis at 0.05 level of significance .

Solution

a)
True, as the reason confidence is directly proportional to the interval

b)

True When P-value is greater than Alpha given, we Fail to reject the null hypothesis