Question

You wish to test the following claim ( H a ) at a significance level of α = 0.002 . H o : μ = 73.8 H a : μ > 73.8 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 31 with mean M = 83.5 and a standard deviation of S D = 16.9 . What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = The p-value is... less than (or equal to) α greater than α 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 greater than 73.8. There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 73.8. The sample data support the claim that the population mean is greater than 73.8. There is not sufficient sample evidence to support the claim that the population mean is greater than 73.8.

Answer 1

Solution :

Given that,

Population mean = = 73.8

Sample mean = M = 83.5

Sample standard deviation = s = 16.9

Sample size = n = 31

Level of significance = = 0.002

This is a right tailed test.

The null and alternative hypothesis is,

Ho: 73.8

Ha: 73.8

The test statistics,

t = ( M - )/ (s/)

= ( 83.5 - 73.8 ) / (16.9 / 31)

= 3.196

P-value = 0.0016

The p-value is p = 0.0016, and since p = 0.0016 < 0.002, it is concluded that the null hypothesis is rejected.

Conclusion:

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population

mean μ is greater than 73.8, at the 0.002 significance level.

There is sufficient evidence to warrant rejection of the claim that the population mean is greater than 73.8.