Question

A simple random sample of size nequals40 is drawn from a population. The sample mean is found to be 104.3​, and the sample standard deviation is found to be 18.2. Is the population mean greater than 100 at the alphaequals0.01 level of​ significance?

Answer 1

Answer:

We conclude that population mean is equal to 100 at the α=0.01 level of​ significance.

Step-by-step explanation:

Given information:

Sample size, n=40

Sample mean=104.3

sample standard deviation, s=18.2

We need to check whether the population mean greater than 100 at the α=0.01 level of​ significance.

Null hypothesis:

$H_0:\mu=100$

Alternative hypothesis:

$H_1:\mu>100$

Let as assume that the data follow the normal distribution. It is a right tailed test.

The formula for z score is

$z=\frac{\overline{x}-\mu}{\frac{s}{\sqrt{n}}}$

$z=\frac{104.3-100}{\frac{18.2}{\sqrt{40}}}$

$z=1.494263$

$z\approx 1.49$

Using the standard normal table the p-value at z=1.49 and 0.01 level of significance is 0.068112.

(0.068112 > 0.01) p-value is greater than α, so we accept the null hypothesis.

Therefore, we conclude that population mean is equal to 100 at the α=0.01 level of​ significance.