Question

This test statistic leads to a decision to...

reject the null

accept the null

fail to reject the null



As such, the final conclusion is that...

There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 88.9.

There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 88.9.

The sample data support the claim that the population mean is not equal to 88.9.

There is not sufficient sample evidence to support the claim that the population mean is not equal to 88.9.

​

Answer 1

There is not sufficient sample evidence to support the claim that the population mean is not equal to 88.9.

Explanation:

We are given the following hypothesis below;

Let
`\mu` = population mean.

So, Null Hypothesis,
`H_0` :
`\mu` = 88.9 {means that the population mean is equal to 88.9}

Alternate Hypothesis,
`H_A` :
`\mu\\eq` 88.9 {means that the population mean is different from 88.9}

The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;

T.S. =
`(\bar X-\mu)/((s)/(√(n) ) )` ~
`t_n_-_1`

where,
`\bar X` = sample mean = 81.3

s = sample standard deviation = 13.4

n = sample size = 7

So, the test statistics =
`(81.3-88.9)/((13.4)/(√(7) ) )` ~
`t_6`

= -1.501

The value of t-test statistics is -1.501.

Also, the P-value of the test statistics is given by;

P-value = P(
`t_6` < -1.501) = 0.094

Since the P-value of our test statistics is more than the level of significance as 0.094 > 0.01, so we have insufficient evidence to reject our null hypothesis as the test statistics will not fall in the rejection region.

Therefore, we conclude that the population mean is equal to 88.9.