Question

You wish to test the following claim ( H a ) at a significance level of α = 0.002 . H o : μ 1 = μ 2 H a : μ 1 ≠ μ 2 You believe both populations are normally distributed, but you do not know the standard deviations for either. However, you also have no reason to believe the variances of the two populations are not equal. You obtain the following two samples of data. Sample #1 Sample #2 103.9 111.8 56.7 84 96.5 86.4 92.3 87.4 82 105.4 83.5 109.7 102.5 78.9 73.2 80.5 90.8 81.8 72 74.8 83.1 75.1 57.2 96.9 69.2 84 57.2 87.5 43.9 89.9 58.4 60.9 56.5 90.8 85.1 68.6 74.4 68 54.1 52.1 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? For this calculation, use the degrees of freedom reported from the technology you are using. (Report answer accurate to four decimal places.) p-value =

Answer 1

Since variances are unknown so we need to test t-test. Test statistics will be

t = (x1bar - x2bar) - (1 - 2) / root s1^2/n1 + s1^2/n2 . standard error = root s1/n1

Now since the data comes from different population , so we will do 2 sample independent t-test.

Please look at the xcel image to understand that how to form data first :-

After that I do a 2 sample independent t test at SPSS.

Before doing 2-sample test we need to check the normality of data. I attach the output of spss where we can see that by seeing the P-value we accept null hypothesis that the data is normal.

P value = 0.567 which is the greater than the critical level p = 0.05 at 95% confidence interval. Please find the output image of normality test below :-

Look at the table above where sig. column is the p-value. & I consider the shapiro-wilk test. U can also consider kolmogorov-smirnov test also.

At last we should test the hypothesis that means of two groups are same.

That is H0 : There is no difference between the mean of 2 sample.

Ha : The means are different.

Please look at the SPSS output below :-

Look at the table of independent sample test. You can consider the case of equality of variances. Now there u see that p value = 0.001. That is the sig. (2-tailed) column. Both in case of Kolmogorov-smirnov & shapiro-wilk test. This p value is less than the critical p value 0.05 , so we reject null hypothesis that means of the two groups are equal at 95% confidence interval. Please see the value of lower confidence limit & upper confidence limit from table also.