Scenario one: Do University of Manitoba students enrolled in Distance Education have different GPAs than students enrolled in regular programs?

The populations being compared here are people living in Winnipeg and the people living in the rest of Canada.

Hypothesis test

H₀: (Null hypothesis): People living in Winnipeg make the same amount of money people living in the rest of Canada make.

H₁: (Alternative hypothesis): People living in Winnipeg make more money than people living in the rest of Canada.

The appropriate hypothesis for this test would be a one–tailed test since the alternative hypothesis has given a one direction outcome. That is, people living in Winnipeg can only be making MORE money THAN people living in the rest of Canada.

The populations being compared here are University of Manitoba students enrolled in regular programs and those enrolled in distance education.

Hypothesis test

H₀: (Null hypothesis): Students of University of Manitoba enrolled in Distance Education and regular programs have equal GPAs.

H₁: (Alternative hypothesis): Students of University of Manitoba enrolled in Distance Education and regular programs have different GPAs.

The appropriate hypothesis for this test would be a two–tailed test since the alternative hypothesis has given a two-sided impression possibility. That is, the students enrolled in distance education could be having higher or lower GPAs than the regular students hence a two-tailed test is used.

Scenario three: Do males laugh more than females?

The populations being compared here are males and females..

H₀: (Null hypothesis): Male and females laugh equally.

H₁: (Alternative hypothesis): Males laugh more than females.

The appropriate hypothesis for this test would be a one–tailed test since the hypothesis has given a direction to the outcome, that is, male laugh more than females.

Question two

Study A

1. Critical value = 5%

1. Critical value = 0.5% on both sides

• Critical value = 5% on both sides

Table 1

Step 1

Population 1: High school students who skateboard to school

Population 2: High school students who do not skateboard to school

Hypothesis test

H₀: (Null hypothesis): Students who skateboard to school and those who do not skateboard have the same coolness.

H₁: (Alternative hypothesis): Students who skateboard to school are cooler than the rest.

Step 2

Calculating the standard error;

Step 3

The study sets the level of significance to be 5%. Since this is a directional hypothesis, only the positive side of the normal curve will be used. For 5% level of significance, the value of Z_score will be 1.64 as read from the normal tables.

Step 4

Determining the sample score of the study we have;

Step 5

Decision rule

The least Z score cut off to reject the null hypothesis was 1.64. The survey’s calculated Z score is 5. This value is greater than the cut-off value of 1.64. The decision therefore is that the alternative hypothesis is statistically significant at 0.05 level of significance.

Scenario two: Does body size affect walking pace?

Question 1

One sample t-test

A research was conducted to establish whether the mean body mass index (BMI) in kg/m3 was 25 among 30 patients who had signs of high blood pressure in a hospital.

The research employed a one-sample t-test since there was only one sample being tested against a mean of 25.

Hypothesis test

H₀: (Null hypothesis): Mean body mass index among the patients is 25 kg/m3.

H₁: (Alternative hypothesis): Mean body mass index among the patients is not 25 kg/m3.

Data

Table 2

Since the sample was 30, the central limit theorem was applied and an assumption of normality arrived at.

Table 3

The survey’s calculated p-value score is .36. This value is greater than the level of significance which is 0.05. The decision therefore is to accept the null hypothesis and reject the alternative hypothesis. The conclusion is that the null hypothesis is statistically significant at 0.05 level of significance.

Question 2

T-test for repeated measures (paired sample t-test)

A research is conducted to test whether heart beat rates are different before having a walk of 300 metres and after.

The appropriate test for the research is a paired sample t-test since we are comparing two variables. That is heart beat rate before and after 300 meters of walk. Since the sample was more than 30, the central limit theorem was applied and an assumption of normality arrived at.

Hypothesis test

H₀: (Null hypothesis): There is no significant difference in heart rate before and after walking for 300 metres.

H₁: (Alternative hypothesis): There is a significant difference in heart rate before and after walking for 300 metres.

Data (first 10)

Table 4

Results table

Table 5

The survey’s calculated p-value score is .00. This value is less than the level of significance which is 0.05. The decision therefore is to reject the null hypothesis and accept the alternative hypothesis. The conclusion is that the alternative hypothesis is statistically significant at 0.05 level of significance.

Question 3

A sample of 46 intern accountants employed in a bank had been trained differently. The first 23 had gone through PC- based training while the other 23 went through traditional lectures. The human resources department wanted to establish whether there is a significant difference in their mean aptitude scores.

The appropriate test was an independent samples t-test since the two samples are independent. They have been drawn from different populations.

Since the sample was drawn from a normally distributed population an assumption of normality was arrived at.

Scenario three: Do males laugh more than females?

Hypothesis test

H₀: (Null hypothesis): There is no difference in mean aptitude test scores between the two groups.

H₁: (Alternative hypothesis): There is a significant difference in mean aptitude test scores between the two groups.

Table 6

Compare the p-value under Lavene’s test for equality of variances with the level of significance (0.05). As can be observed, the p-value calculated (0.002) is less than the level of significance (0.05). The decision is therefore to reject the null hypothesis. The conclusion is that the alternative hypothesis is statistically significant at 0.05 level of significance.

Question 1

The appropriate test was an analysis of variance since the variables were more than two.

Dependent variable: Walking time

Independent variables: Body size

Table 7

Table 8

As can be observed above, the kurtosis values are near zero indicating normality.

H₀: (Null hypothesis): All the mean times in all the four groups are equal.

H₁: (Alternative hypothesis): At least one mean is different

Table of results

Table 8

As can be observed, the p-value calculated (0.00) is less than the level of significance (0.05). The decision is therefore to reject the null hypothesis. The conclusion is that the alternative hypothesis is statistically significant at 0.05 level of significance.

Question 2

Factorial anova

A study is conducted to establish the effect of gender (male and female) and body size (obese and normal) on time used to walk 200 meters. It is hypothesized that gender and body size affect the speed at which people walk. So the research question is, does gender or body size affect speed of walking?

Dependent variable: Walking time

Independent variables: Gender and body size

Factorial anova was appropriate since the study focused on establishing whether there is a difference between mean time taken to walk 200 meters between the obese and normal individuals.

Hypothesis test 1

H₀: (Null hypothesis): The average amount of time taken to walk between the normal and obese groups is the same.

H₁: (Alternative hypothesis): The average amount of time taken to walk between the normal and obese groups is not the same.

Hypothesis test 2

H₀: (Null hypothesis): The average amount of time taken to walk between the males and females is the same.

H₁: (Alternative hypothesis): The average amount of time taken to walk between the males and females is not the same.

Table 9

Table 10

The factorial ANOVA shows that there was no main effect of body size on time taken (.24, p > .05). There was also no main effect of gender on time taken (.17, p > .05).

Question one: One sample t-test

There was also a significant interaction between the two factors (gender and body size) (.16, p > .05).

Plot of means of interaction effects

Interpretation

• The main effect of time: Normal people do not have difference in walk time regardless of gender. 

PART FOUR

NON-PARAMETRIC TESTS

Question 1

Chi-square test for goodness of fit

A research was conducted on 30 individuals after 3 companies advertised their brands of new washing powders. The 30 individuals were asked which washing powder they would prefer. It is assumed that before the campaign preference for the washing powders was the same across the three. The research question therefore is, did the advertising campaign have an effect on the consumers’ preference on the washing powders?

Chi-square test for goodness of fit was appropriate in this research since it was comparing effect of a factor on proportions before and after.

The washing powders were A, B and C. They were chosen as in the table below;

Table 11

Hypothesis test 1

H₀: (Null hypothesis): There was no effect on consumer preference of the three washing powders after the campaigns

H₁: (Alternative hypothesis): There was a significant effect on consumer preference of the three washing powders after the campaigns.

Table 12

Table 13

As can be observed from the results table, the p-value (1.22) is greater than significance level (0.05). Therefore there is sufficient evidence to reject the null hypothesis. The conclusion is that the campaigns had a significant effect on consumers’ preference of the three washing powders.

Question 2

Chi-square test for independence

For a research to predict the demand for analysis package courses in a college, it was presumed or hypothesized that students’ undergraduate degree courses affected their choice of analysis packages. That is some degree courses would tend to have a preference for certain analysis packages. Therefore, are the two variables independent?

The chi-square test for independence is appropriate in this question since it involved two qualitative variables (the analysis software and degree courses).

The variables are degree course and analysis software.

The below contingency table gives a summary of the data;

Table 14

Hypothesis test

H₀: (Null hypothesis): The two variables (degree course and analysis software) are independent

H₁: (Alternative hypothesis): The two variables (degree course and analysis software) are dependent

Results table

Table 15

As can be observed from the results table, the p-value (.63) is greater than significance level (0.05). Therefore there is sufficient evidence to reject the alternative hypothesis. The conclusion is that the two variables are independent.

Question 3

For a research to assess the effectiveness of advertising, two products were compared (product X and product Y). The products were advertised after which 30 participants allowed to rate their chances of purchasing the products. The rating was between 1 and 5 with 5 indicating “will definitely buy”. 15 participants rated X and the other rated Y.

This test was appropriate since the variables involved ordinal scale and they were also not normally distributed.

Dependent variable: Likelihood of purchasing

Independent variables: advertising

Hypothesis test

H₀: (Null hypothesis): Advertising did not have an effect on the likelihood of purchase.

H₁: (Alternative hypothesis): Advertising had a significant effect have an effect on the likelihood of purchase.

Table of results

Table 16

Table 17

As can be observed from the results table, the p-value (.83) is greater than significance level (0.05). Therefore there is sufficient evidence to reject the alternative hypothesis. The conclusion is that the two variables are independent.