A simple random sample of 64 items from a population with standard deviation $\sigma=4$ resulted in a sample mean of 35. What is the margin of error for the population mean at a 95% confidence level? (Given $Z_{0.025}=1.96$)

A random sample of 100 individuals provides 25 positive responses.

Then the point estimate of the population proportion with "positive" responses is:

Which of the following are correct about t-test statistics?

(A) The mean of t-test distribution is 0.

(B) It depends on the degrees of freedom.

(C) It depends on population standard deviation.

(D) With more degrees of freedom, it closely resembles standard normal distribution.

Choose the correct answer from the options given below:

The marks obtained by five students in a test of Applied Mathematics carrying 100 marks are 49, 58, 67, 92, 99. Then the point estimate of the population mean is

Which one of the following statement is not correct?

Consider the following hypothesis test :

$H_0: \mu \le 35$

$H_a: \mu > 35$

A sample of 49 provided a sample mean of 38.2 The population standard deviation is 8. The value of test-statistic is,

If we reject the null hypothesis when it is true, we might be making