Consider the following hypothesis

$H_0: \mu = 315$ and $H_a: \mu \neq 315$

A sample of 60 provided a sample mean of 324.6. The standard deviation ($\sigma$) is 14 and level of significance $\alpha = 0.05$. Then the confidence interval is:

[Given: $Z_{a/2}{\frac{14}{\sqrt60}} = 3.54$]

Which of the following points describe the concept of population in inferential statistics ?

A. It is a collection of all elements having same characteristics.

B. A survey done on the total population is not accurate.

C. Population focuses on the identification of the characteristic.

D. Population focuses on drawing inference about the sample.

Choose the correct answer from the options given below:

Which of the following are types of "statistical inferences"?

(A) Point estimation

(B) Interval estimation

(C) Marginal estimation

(D) Hypothesis testing

Choose the correct answer from the options given below:

A machine has been producing steel tubes of mean inner diameter of 2 cm. A sample of 10 tubes gives an inner diameter of 2.01 cm and a standard deviation of 0.063 cm. Test the hypothesis that the machine is working in the proper order at 5 % level of significance and answer, which of the following statements are correct?

[Given that : t₉(0.05) = 2.262]

(A) The value of the test statistic is t = 0.476.

(B) The null hypothesis is rejected at 5 % level of significance.

(C) The null hypothesis is accepted at 5 % level of significance.

(D) The degree of freedom is 10.

Choose the correct answer from the options given below:

Match List-I with List-II

Choose the correct answer from the options given below:

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

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