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]

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:

Consider the following hypothesis test,

$H_0: \mu = 15$

$H_a: \mu ≠ 15$

A sample of 50 provided a sample mean of 14.15. If the sample standard deviation is 3, then the value of the test statistic t0-test is

For the following data:

The sample statistic t follows t-distribution with 'm' degrees of freedom, then m is equal to

The monthly salaries of workers in a garment factory are normally distributed. The mean salary is ₹ 10,000 and standard deviation is ₹ 625. If 2,500 workers are getting salary less than ₹ 10,000, then the total number of workers in the factory is:

If the sample size ($n$) is 32 in testing of hypothesis by t-test, then the degree of freedom ($\gamma$) is equal to :

If a sample has 'n' observation $x_1$, $x_2$ ............. $x_n$ with 'm' constraints on these values then degree of freedom of sample statistic is: