Question one
The mean of the Test variable is and its standard deviation is . For the performance variable the mean is and the standard deviation is . The histograms for both the performance and test variables are shown below. The performance histogram has a bimodal distribution while the test histogram is skewed to the left.
Question two
Step 1: Defining the null and the alternate hypotheses. The alternate hypothesis in this case is the research hypothesis or rather the claim.
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Step 2: Determining the level of significance ; which we have been given as .
Step 3: Calculating the test statistic
The formula is given by
Step 4: P-value
The p-value from the normal distribution table and also using the NORMSDIST function in excel is . Using the alpha value given of , we notice that the p-value is less than the alpha value.
Step 5: Conclusion
Since the p-value is less than the alpha value, we reject the null hypothesis and accept the alternate hypothesis. We therefore can conclude that high school teachers who exercise regularly have lower stress scores.
The 95% confidence interval
Since it is a 95% confidence interval, the z score is 1.96. The CI therefore can be found from
Therefore, there is a 95% chance that the average value of the stress test scores of high school teachers who exercise lie between values and .
Question three
Using t-test we can determine whether there is a statistically significant difference between the means of the Pre-ride Attitudes and the Post-ride Attitudes. For the purposes of the hypothesis testing we are going to do the Pre-ride Attitudes will be denoted as 1 while the Post-ride Attitudes as 2. First, we determine the null hypothesis and the alternate hypothesis. In this case, the null hypothesis will be there is no significant difference between the means of the participants’ pre-ride Attitude and their post-ride Attitudes. The alternate hypothesis is that there is a difference between the two means.
Secondly, we determine the degrees of freedom for the t-test. The degrees of freedom is determined by the formula below.
The third step will be to determine the t-critical value. Since we are using an alpha of , we can find the t critical value that will be used to gauge our t-test statistic. We find the t-critical value from the t-table. The t-critical value using as the degrees of freedom and 0.05 as the alpha value, we find that the t-critical value is This t-critical value is the value that if it is surpassed by the t-test statistic we reject the null hypothesis and if the t-test statistic is smaller than it we fail to reject the null hypothesis.
The fourth step will be to calculate the t-test statistic. In this case, we will use the formulae:
The fifth step is to derive a conclusion from the calculated t-statistic. From the above calculations we notice that the t-statistic is . This value is larger than the t-critical value and therefore, we reject the null hypothesis and accept the alternate hypothesis which is that there is a statistically significant difference between the Pre-ride Attitudes and the Post-ride Attitudes. This therefore means that riding the train has an impact on the attitudes of the participants.
Question four
In this case, we use the t-test as well only that it will be a one tail test (right-tailed test). We will group that data according to those who did not attend (control condition) the seminar and those who attended the seminar (experimental condition) with groups being given the labels 1 and 2 respectively. First, we determine the null and the alternate hypotheses. The null hypothesis in this case is that the means of group 1 and group 2 have no statistically significant difference between each other. The alternate hypothesis which is the research hypothesis or rather the claim is that the means of the two groups have a statistically significant difference with mean of group 2 being larger than the mean of group 1.
The second step will be to determine the degrees of freedom for the t-test. It is calculated as:
The third step will be to determine the t-critical value. We use as the alpha and 6 as the degree of freedom to find the critical value on the t-distribution table. In this case the t-critical value for the right-tailed test is .
The fourth step will be to calculated the t-statistic. The t-statistic can be calculated from the formula below:
The fifth and the last step is to draw a conclusion based on the t-statistic and the t-critical value. Since the calculated t-statistic is greater than the t-critical value we reject the null hypothesis and therefore accept the alternate hypothesis. Therefore, the seminars are effective and increase employees’ motivation.
