Question

An educator wanted to look at the study habits of university students. As part of the research, data was collected for three variables – the amount of time (in hours per week) spent studying, the amount of time (in hours per week) spent playing video games and the GPA – for a sample of 10 male university students. As part of the research, a 95% confidence interval for the average GPA of all male university students was calculated to be: (2.95, 3.10).

Which of the following statements is true?

a. In construction of the confidence interval, a z-value with 10 degrees of freedom was used.
b. In construction of the confidence interval, a z-value was used.
c. In construction of the confidence interval, a t-value with 10 degrees of freedom was used.
d. In construction of the confidence interval, a t-value with 9 degrees of freedom was used.

Answer 1

c. In construction of the confidence interval, a t-value with 10 degrees of freedom was used.

Explanation:

Confidence Interval is the estimated value that is computed from the statistic of data which is observed. The range value is plausible for unknown parameters. The t-value with 10 degrees of freedom was used in the given scenario because the data observed of 10 male university students. To find the critical value the confidence interval value is observed through the t-value table.

Answer 2

option A

Explanation:

Since All values in confidence interval are less than 3.12, we do not have sufficient evidence

as degree of freedom is sample size -1 ; hence df =20-1 =19

In construction of the confidence interval, a t-value with 19 degrees of freedom was used therefore option b, c and d are incorrect

also, In construction of the confidence interval, a z-value with 10 degrees of freedom was used