Question

2.3. Each of the following scenarios presents a claim by a researcher. Assume that the sample sizes in each case was in the range of 20 to 25 observations per sample in each case. Answer the following for each scenario:

(i) state the appropriate null (HO) and alternate hypothesis (HA) in symbolic form (e.g. Hx : Meanleft = Meanright);

(ii) indicate whether it is a 1or 2-tailed test, and if a 1-tailed tests which tail is the area of rejection at.

A. Outside of the nesting season, male and female Robins do not differ in weight. An ornithologist thought however that females gained extra weight prior to nesting. She captured and weighed 20 adult females (F) and 22 males (M) from the same location just as they were started to build nests.wanted to know if this was also true during the nesting season.

B. A resident of Peterborough thinks the city is unusual in that the north end of the city (near Trent University) gets less rainfall than the south end (of the city (near Peterborough Airport). Data were collected for all rain events greater than 4 mm from weather stations at the University (TU) and the airport (PA) from April 1 to November 30 2019.

C. Whether the intensity of rain events (cm/hr) in August (AUG) differ from those in May (MAY) in Peterborough county.

D. A Professor wonders whether it is true that students actually spend more time (hours per week) on course work (ie “attending lectures” and doing assignments) in his online course(ON) compared to the same course taught face-to-face (F2F) in the same semester. He surveyed 25 students from each of the two courses.

Answer 1

For the given scenarios:

A. Outside of the nesting season, male and female Robins do not differ in weight. An ornithologist thought however that females gained extra weight prior to nesting. She captured and weighed 20 adult females (F) and 22 males (M) from the same location just as they were started to build nests.wanted to know if this was also true during the nesting season.

Here, the parameter of interest for the ornithologist is the mean weight of female and male robins, prior to nesting. (i) Let and denote the mean weight of female and male robins, prior to nesting, respectively. We need to test:

Vs

(ii) We may state that the test is one-tailed - right tailed test (> in the alternative), to be specific; with the rejection region being the extreme values at the right tail of the distribution curve.

B. A resident of Peterborough thinks the city is unusual in that the north end of the city (near Trent University) gets less rainfall than the south end (of the city (near Peterborough Airport). Data were collected for all rain events greater than 4 mm from weather stations at the University (TU) and the airport (PA) from April 1 to November 30 2019.

Here, the parameter of interest for the resident is the average rainfall (in mm) received by the north and south end of Peterborough city.

(i) Let and denote the average rainfall (in mm) received by the north and south end of Peterborough city, respectively. We need to test:

Vs

(ii) We may state that the test is one-tailed - left tailed test (< in the alternative), to be specific; with the rejection region being the extreme values at the left tail of the distribution curve.

C. Whether the intensity of rain events (cm/hr) in August (AUG) differ from those in May (MAY) in Peterborough county.

Let and denote the average rainfall (in mm) received in August and May in Peterborough city, respectively. We need to test:

Vs

(ii) We may state that the test is two-tailed (since no specific direction is mentioned in the problem); with the rejection region being the extreme values at both the tail of the distribution curve.

D. A Professor wonders whether it is true that students actually spend more time (hours per week) on course work (ie “attending lectures” and doing assignments) in his online course(ON) compared to the same course taught face-to-face (F2F) in the same semester. He surveyed 25 students from each of the two courses.

Here, the parameter of interest for the Professor is the average number of hours spent by students on course work (ie “attending lectures” and doing assignments) in his online course(ON) compared to the same course taught face-to-face (F2F) in the same semester.

(i) Let and denote the average number of hours spent by students on course work (ie “attending lectures” and doing assignments) in his online course(ON) compared to the same course taught face-to-face (F2F) in the same semester, respectively. We need to test:

Vs

(ii) We may state that the test is one-tailed - right-tailed test (> in the alternative), to be specific; with the rejection region being the extreme values at the right tail of the distribution curve.