Answer:
Step-by-step explanation:
Hello!
To apply a t-test for a hypothesis test, the following conditions:
1. Variables of interest should be at least of an ordinal scale.
2. The sampling method should be at least SRS, the sample should be representative of the population.
3. The data, when plotted, should have a normal distribution.
Now you have to check in the scenarios if the conditions are met:
A)In a random sample of 100 university students, the distribution of time spent at university recreational facilities is strongly skewed to the right.
1. The variable is X: Time spent at the university recreational facilities.
The variable "time" is at least ordinal, so this condition checks.
2. The sample was randomly taken so this condition checks.
3. The data is strongly skewed to the right, the normal distribution is symmetrical, so is highly unlikely that this data set has a normal distribution.
⇒ A t-test is not applicable in this scenario.
B) In a random sample of 50 university students (37 females and 13 males), the distribution of time spent at university recreational facilities is strongly skewed to the right for females but not strongly skewed for males.
1. In this case, you have two groups of interest, to each group you'll measure the variable X: Time spent at the university recreational facilities.
The variable "time" is at least ordinal, so this condition checks.
2. The samples "male students" and "female students" were randomly taken so this condition checks.
3. In this scenario, you have two populations of interest 1. Male university students and 2. Female university students. Both populations should be normal to apply the t-test.
The distribution for the females has strongly skewed to the right.
The distribution for males is slightly skewed.
The distribution for the females is strongly skewed, then there is no possibility for it to be normal.
⇒ A t-test is not applicable in this scenario.
C) In a study of 100 brother-sister sibling pairs at the university, the distribution of time spent at university recreational facilities for the 100 males is compared to the 100 females; both distributions are fairly normal.
1. In this case, this is an example of a "paired sample" because the experimental units are dependent. (Think about the relationship the sibling pair may have if they get along well, then itis likely that they spend time together in the recreational facilities, on the other hand, if their relationship is not so good it is more likely that the presence of one of the siblings in the facilities will make the other one spend less time in it.)
The variable measured for each member of the "sibling pair" will be X: Time spent at the university recreational facilities, and the study variable, in this case, will be determined by the difference between the times measured for both siblings Xd: Difference between the time the brother and the sister spend in the university recreational facilities.
The variable "time" is at least ordinal, so this condition checks.
2. The sample of "brother-sister sibling pair" was randomly taken so this condition checks.
3. If X₁: time the brother spends in the recreational facility and X₂: time the sister spends in the recreational facility has a normal distribution. Then the "variable difference", Xd= X₁ - X₂, resulting out of them will also have a normal distribution.
The normality condition checks.
⇒ You can apply the t-test in this scenario.
I hope this helps!
