Question

1. Given the following data, test at the 0.05 level of significance to see if the number of dogs treated at two different vet clients differs. Assume variances are equal.
Clinic A (doges treated per 10 randomly selected day); 10, 11, 15, 4, 8, 9, 14, 5, 18, 20 Clinic B (dogs treated per 7 randomly selected day): 11, 16, 15, 18, 14, 16, 18
2. Given the following data, test to see if the company with newer technology has greater output than the company with older technology. Test at the 0.05 level of significance and do not assume equal variances.
Company A (with new technology): 1123, 1120, 1000, 1500, 1500,
Company B (with old technology): 1000, 990, 890, 930, 870
Test for Two Variances
3. For both SPSS problems 1 & 2 above, use the Levene's F-value provided in the output to test to see if variances are equal between the two groups being evaluated.

Answer 1

The data is added into SPSS as follows:

The test is run from Analyse -> Compare Means -> Independent two sample tests. The grouping variable is the VAR 002 in our data. The output of SPSS is as follows:

Assuming variances are equal, t - -1.865 and p= 0.082. Hence, we cannot reject the null hypothesis and can conclude that the mean number of dogs treated at two different vet clients do not differ.

3. a) From Levene's test,

Null Hypothesis: The population variances are equal

F-value = 4.628 and p= 0.048

As the p-value<0.05, we can reject the null hypothesis and say that the population variances are not similar for both the groups.

2. We will run the test similarly as in Question 1. The output of the SPSS is:

Assuming variances are not equal,

t = 2.890, We will compute the one-tailed p-value which is 0.019. As the p-value<0.05, we can reject the null hypothesis. We can say that the newer technology has greater output then the older technology.

3. b) From Levene's test,

F = 22.941, p = 0.001

As the p-value<0.05, we can reject the null hypothesis. Hence, we can say that the variances of both the population groups are not similar.