You wish to test the following claim (Ha) at a significance level of a0.02 Hospi

Question

You wish to test the following claim (Ha) at a significance level of a0.02 Hospi 82.7 Ha:u>82.7 You believe the population is normally distributed, but you do not know the standard deviation. You obtain the following sample of dat Column A Column B Column C Column D 113.1 116.8 71.7 81.5 89.3 99.3 97.7 89.8 72.6 131.5 90.3 64.5 94.5 100.4 114 120.3 114.9 120.3 76.3 114.9 91.9 119.1 124.7 109.9 121.6 97.1 58.2 66.9 89.8 100.4 124.7 104.5 69 91.9 63.2 84.4 What is the critical value for this test? (Report answer accurate to three decimal places) critical value What is the test statistic for this sample? (Report answer accurate to three decimal places) test statistic

Explanation / Answer

Solution:

Here, we have to use one sample t test for the population mean. The null and alternative hypotheses for this test are given as below:

H0: µ = 82.7

Ha: µ > 82.7

This is a one tailed test. This is an upper tailed test. (Right tailed test)

We are given

Level of significance = ? = 0.02

From given data, we have

Sample size = n = 36

Sample mean = Xbar = 96.97222222

Sample standard deviation = S = 20.32592449

Degrees of freedom = n – 1 = 36 – 1 = 35

Level of significance = ? = 0.02

Critical value = 2.133

Test statistic formula is given as below:

t = (Xbar - µ) / [S/sqrt(n)]

t = (96.97222222 – 82.7) / [20.32592449/sqrt(36)]

t = (96.97222222 – 82.7) /3.3877

t = 4.2130

Test statistic = 4.213

P-value = 0.0001

(by using t-table or excel)

P-value < ? = 0.02

So, we reject the null hypothesis

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