A simple random sample of 49 items from a population with standard deviation, σ = 6 resulted in a sample mean of 32. At 95% confidence level, the margin of error is (Given $Z_{0.025} = 1.96$)

A company has been producing steel tubes of mean inner diameter of 3 cm. A sample of 17 tubes gives an inner diameter of 3.01 cm and a standard deviation of 0.064. Then the value of the t-test statistic is:

Which of the following are correct?

(A) A statistical hypothesis is a statement about the population parameter which may be true or false.

(B) In a statistical hypothesis testing procedure, a Type I error is made when the null hypothesis is accepted when it is false.

(C) In a statistical hypothesis testing procedure, a Type II error is made when the null hypothesis is rejected when it is true.

(D) The number of degrees of freedom of a statistic is the number of independent variates used to compute that statistic.

Choose the correct answer from the options given below:

A company produces an item M whose mean sales per shop per month was found to be 84 dozens. After an advertisement, a sample of 26 shops was taken and mean sales was found to be 80 dozens with standard deviation of 9. Based on this data, which of the following is true?

(Given $t_{25}(0.05) = 2.06$)

[t = t-test statistic]

Which of the following is not correct about the Central Limit Theorem?

The following data are from a simple random sample: 8, 11, 13, 10, 13, 17. The point estimate of the population mean is:

Consider the following hypothesis test:

$H_0: \mu \leq 25$

$H_a: \mu > 25$

A sample of 25 provided a sample mean of 27.80. The population standard deviation is 5, then the value of the test statistic is