In each of the following scenarios, researchers plan to conduct either a hypothesis test for a population mean or for the difference in two population means. Are the conditions for use of a T-model met?
1. In a random sample of 100 university students, the distribution of time spent at university recreational facilities is strongly skewed to the right. [ Select ] ["Conditions met; proceed with the hypothesis test.", "Conditions not met; do not proceed with the hypothesis test."]
2. 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. [ Select ] ["Conditions met; proceed with the hypothesis test.", "Conditions not met; do not proceed with the hypothesis test."]
3. 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.

Question

10-12-2022
Mathematics

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In each of the following scenarios, researchers plan to conduct either a hypothesis test for a population mean or for the difference in two population means. Are the conditions for use of a T-model met?
1. In a random sample of 100 university students, the distribution of time spent at university recreational facilities is strongly skewed to the right. [ Select ] ["Conditions met; proceed with the hypothesis test.", "Conditions not met; do not proceed with the hypothesis test."]
2. 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. [ Select ] ["Conditions met; proceed with the hypothesis test.", "Conditions not met; do not proceed with the hypothesis test."]
3. 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.

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rafikiedu08 rafikiedu08 · Answer 1 · 2022-12-16T10:16:10+01:00

In the following first scenario the conditions for the t-test is not met for the difference in populations mean so the hypothesis test cannot be done.

1)The distribution of time spent at university recreational facilities is considerably skewed to the right in a random sample of 100 university students.

The variable is X, which stands for time spent at the university's leisure facilities.

Because the variable "time" is at least ordinal, this criterion is satisfied.

The sample was drawn at random, hence this requirement is met.

The data is heavily skewed to the right, the normal distribution is symmetrical, and this data set is highly unlikely to have a normal distribution.

2)The distribution of time spent at university recreational facilities is highly skewed to the right for females but not strongly skewed for males in a random sample of 50 university students (37 females and 13 males).

In this scenario, you have two groups of interest, and the variable X: Time spent at the university recreational facilities will be measured for each group.

Because the variable "time" is at least ordinal, this criterion is satisfied.

The samples "male students" and "female students" were randomly taken so this condition tests.

You have two populations of interest in this case. Male university students and female university students are divided into two groups. To use the t-test, both populations must be normal.

The distribution for the females has strongly skewed to the males have a somewhat skewed distribution.

If the distribution of females is substantially skewed, it is impossible for it to be normal.

In this case, a t-test is not appropriate.

3)Because the experimental units are dependent, this is a "paired sample" situation. (Consider the sibling pair's relationship; if they get along well, it is more likely that they will spend time together in the recreational facilities; if their relationship is not so good, it is more likely that the presence of one of the siblings in the facilities will cause the other to spend less time there.)

X will be the variable measured for each member of the "sibling pair": Time spent at university recreational facilities, and the research variable in this case, will be defined by the difference in times measured for both siblings.

The normality condition checks.

so the t-test in this scenario can be applied.

To learn more about hypothesis test visit:

https://brainly.com/question/17099835

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