A sample of size 9 from a normal population with sample mean $\bar{X} = 15.8$ and population estimated standard deviation $\sigma = 3.21$, then 99% confidence interval for population mean is : $(Use: t_8(0.01) = 3.335)$

The following data are from a random sample: 5,8,10,7,10,14, then the point estimate of the population standard deviation is

Which of the following statements are TRUE?

(A) The variable t of t-distribution ranges from $-\infty$ to $\infty$.

(B) The probability curve of the t-distribution is symmetric about the line $t=0$

(C) The variance of the t-distribution is greater than one.

(D) As the number of degrees of freedom decreases, the t-distribution curve moves closer to the standard normal probability curve.

Choose the correct answer from the options given below:

Consider the following hypothesis test:

$H_0: \mu = 18$

$H_1: \mu \neq 18$

If a sample of 48 provided a sample mean $\bar{x} = 17$ and a sample standard deviation $\sigma = 4.5$, then the value of the t-test statistic is:

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]

For the data from the simple random sample as: 5, 8, 10, 7, 18, 12

The point estimate of the population standard deviation is

The following data is from a simple random sample :

$15,23, x, 37,19,32$

If the point estimate of the population mean is $23$, then the value of $x$ is :