The point estimate of the population standard deviation for the random sample 5, 8, 10, 7, 10, 14 is:

A random sample of size 16 has 53 as mean. The sum of the squares of the deviations taken from mean is 150. If the population mean is 56 then the value of t-test statistic is:

A simple random sample of 64 items from a population with standard deviation $\sigma=4$ resulted in a sample mean of 35. What is the margin of error for the population mean at a 95% confidence level? (Given $Z_{0.025}=1.96$)

Which of the following is not a rejection rule for one sample t-test: (Where α is the level of significance)

(A) Reject null hypothesis $H_0$ : if $t \leq -t_\alpha$.

(B) Reject null hypothesis $H_0$ : if $t \geq -t_\alpha$.

(C) Reject null hypothesis $H_0$ : if $t \geq t_\alpha$.

(D) Reject null hypothesis $H_0$ : if $t \leq -t_{\alpha/2}$ or $t \geq t_{\alpha/2}$.

Choose the correct answer from the options given below:

Match the LIST-I with LIST-II

Choose the correct answer from the options given below:

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

Let two independent random samples of sizes $n_1$ and $n_2$ respectively have been drawn from the same normal population. Let $\overline{X_1}$ and $\overline{X_2}$ be the means and let $s_1$ and $s_2$ be their standard deviations. In order to test whether the the two sample means $\overline{X_1}$ and $\overline{X_2}$ differ significantly or not, the $t$-test statistic is given by