Question

For Questions 1 and 2, include all Steps of Hypothesis Testing listed below in bold. For each problem, use the p-value

from SPSS to determine whether to reject or not reject the null hypothesis and don’t forget to

indicate your conclusion about whether there is a significant difference.

1)State your hypotheses: H0 and H1

2)Select the appropriate statistical test

3)Indicate whether test is directional or non-directional

4)Specify a, N, and df (if appropriate)

5)Do your calculations

6)Determine critical value(s) for test statistic

7)Make the appropriate decision based on Steps5 & 6 to reject or fail to reject your null hypothesis

8) State conclusion (interpret results) in words

1. An instructor believed that the students who earn a C or higher differ in the number of hours they

spend studying, compared to students who receive a D or F. She collected the following data on

two independent samples of students from a class of 150 students.

Course Grade

Hours Spent Studying

A, B, or C:

9, 5, 12, 4, 7, 5, 4, 6, 1, 8

D or F:

3, 3, 1, 4, 0, 2, 3, 1, 4, 3

Using SPSS and

alpha = .05, conduct an appropriate statistical test. There is no data file; you must

enter the data yourself. Submit all written steps and the actual SPSS output.

2. An investigator wishes to compare the effects of two different training methods on the

performance of a particular task. He recruits 16 participants and randomly assigns them to

Training Method 1 or Training Method 2. Assume that the following results are obtained, where

higher scores indicate better performance.

Training Method

Performance

Method 1:

7, 8, 10, 14, 12, 13, 15, 16

Method 2:

5, 3, 12, 10, 11, 10, 12, 12

Conduct an appropriate statistical test using SPSS and alpha = .05. There is no data file; you must enter the data yourself. Submit all written steps and the actual SPSS output.

Answer 1

Solution:-

1)

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u₁ = u ₂
Alternative hypothesis: u₁ u ₂

Note that these hypotheses constitute a two-tailed test.  

Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a two-sample t-test of the null hypothesis.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = sqrt[(s₁²/n₁) + (s₂²/n₂)]
SE = 1.06092
DF = 18
t = [ (x₁ - x₂) - d ] / SE

t = 3.49

where s₁ is the standard deviation of sample 1, s₂ is the standard deviation of sample 2, n₁ is the size of sample 1, n₂ is the size of sample 2, x₁ is the mean of sample 1, x₂ is the mean of sample 2, d is the hypothesized difference between the population means, and SE is the standard error.

Since we have a two-tailed test, the P-value is the probability that a t statistic having 18 degrees of freedom is more extreme than -3.49; that is, less than -3.49 or greater than 3.49.

Thus, the P-value = 0.003

Interpret results. Since the P-value (0.003) is less than the significance level (0.05), we cannot accept the null hypothesis.

From the above test we have sufficient evidence in the favor of the claim that the students who earn a C or higher differ in the number of hours they spend studying, compared to students who receive a D or F.