CUET Mathematics 2025 27 May Shift 1 PYQs

A machine has been producing steel tubes of mean 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:

Consider the following hypothesis test:

$H_0: \mu \leq 16$

$H_a: \mu > 16$

A sample of 25 provided a sample mean $\bar{x} = 17$ and a sample standard deviation $s = 3.5$, then the value of the test statistic in $t$-test is:

Rajesh calculated 95% confidence level. What does he mean by that?

(A) He can be 95% confident that his sample will include the population parameter.

(B) He can be 95% confused that his sample will include the population parameter.

(C) He can be 5% confident that his sample will not include the population parameter.

(D) He can be 5% confident that his sample will include the population parameter.

Choose the correct answer from the options given below: