2. A teacher wants to investigate whether there is a difference between male and female students in the amount of time they spend studying for statistics. The table below shows the amount of time students spend studying statistics each week. The amounts of time spent studying are normally distributed.
Male Female
27 25
25 29
19 18
10 23
16 20
17 15
15 19
a. What statistical test should be used to analyze the data?
b. Is this a one- or two tailed test?
c. Identify H0 and Ha for this study.
d. Conduct the appropriate analysis. Should H0 be rejected?
Ho: mean1 = mean2
Ha: mean1 ≠ mean2
Does that indicate one-tailed or two?
Find the mean first = sum of scores/number of scores
Subtract each of the scores from the mean and square each difference. Find the sum of these squares. Divide that by the number of scores to get variance.
Standard deviation = square root of variance
Z = (mean1 - mean2)/standard error (SE) of difference between means
SEdiff = √(SEmean1^2 + SEmean2^2)
SEm = SD/√(n-1)
If only one SD is provided, you can use just that to determine SEdiff.
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to your Z score.
a. The appropriate statistical test to analyze the data in this scenario is the independent samples t-test. This test is used when comparing the means of two independent groups, in this case, male and female students.
b. This is a two-tailed test. A two-tailed test is used when we want to consider the possibility of a difference in either direction (i.e., whether males spend more or less time studying than females).
c. H0 (null hypothesis): There is no difference in the amount of time spent studying for statistics between male and female students.
Ha (alternative hypothesis): There is a difference in the amount of time spent studying for statistics between male and female students.
d. To conduct the independent samples t-test and determine whether H0 should be rejected, you would follow these steps:
1. Calculate the mean (average) time spent studying for each group (male and female).
2. Calculate the standard deviation for each group.
3. Calculate the t-value using the following formula: t = (mean1 - mean2) / sqrt((s^2/n1) + (s^2/n2)), where mean1 and mean2 are the means, s^2 is the pooled variance, and n1 and n2 are the sample sizes.
4. Determine the degrees of freedom (df) using the formula: df = n1 + n2 - 2, where n1 and n2 are the sample sizes.
5. Look up the critical t-value for the desired significance level and degrees of freedom (df), typically at a significance level of 0.05.
6. Compare the calculated t-value to the critical t-value. If the calculated t-value exceeds the critical t-value, H0 can be rejected. If not, H0 cannot be rejected.
It is not possible to conduct the analysis and determine whether H0 should be rejected without the sample sizes and other necessary statistics (standard deviation, significance level, etc.).