Question

Problem G: A random sample of size n = 56 is selected from a non-normal population with mean y = 24 and standard deviation o = 12.5. (33) Refer to Problem G. Describe the shape of the sampling distribution. (1) Non-normal. (3) Approximately normal. (2) Exactly normal. (4) Uniform. (34) Refer to Problem G. What is the mean of the sampling distribution? (1) 12.5 (2) 24 (3) 1.67 (4) 3.2 (35) Refer to Problem G. Calculate the standard error of the sample mean. (1) 1.67 (2) 0.223 (3) 12.5 (4) 24

Answer 1

Problem G

A random sample of size n=56 is selected from a non normal population with mean = 24 and standard deviation = 12.5.

Question 33

The sampling distribution is actually the probability distribution of the sample mean of the problem.

Now, as the sample size, which is 56, is larger than 30, we can use the Central Limit Theorem.

The Central Limit Theorem states that the shape of the sampling distribution is approximately normal, when the sample size is large enough.

So, the answer is

The shape of the sampling distribution is option (3) Approximately normal.

Question 34

Given that the population mean is 24.

This means that, the mean of the sampling distribution, which is same as the population mean, is also 24.

The answer is

The mean of the sampling distribution is option (2) 24.

Question 35

Now, the standard error of the sampling mean is given by the formula

$s.e.=\frac{\sigma}{\sqrt{n}}$

Where, n is the sample size and sigma is the population standard deviation.

So, in this problem,

$\sigma=12.5$

$n=56$

So,

12.5 V56

$=1.6703$

The answer is

The standard error of the sample mean is approximately option (1) 1.67.