Question

 Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable.

 (a) The number of points scored during a basketball game.

 (b) The amount of rain in City B during April.

 (a) Is the number of points scored during a basketball game discrete or continuous?

 A. The random variable is discrete. The possible values are x≥0.

 B. The random variable is continuous. The possible values are x =0, 1, 2.....

 C. The random variable is discrete. The possible values are x =0, 1, 2,....

 D. The random variable is continuous. The possible values are x≥0.

 (b) Is the amount of rain in City B during April discrete or continuous?

 A. The random variable is continuous. The possible values are r=1, 2, 3. ....

 B. The random variable is continuous. The possible values are r≥0.

 C. The random variable is discrete. The possible values are r=1, 2, 3....

 D. The random variable is discrete. The possible values are r≥0.

 Two researchers conducted a study in which two groups of students were asked to answer 42 trivia questions from a board game. The students in group 1 were asked to spend 5 minutes thinking about what it would mean to be a professor, while the students in group 2 were asked to think about soccer hooligans. These pretest thoughts are a form of priming. The 200 students in group 1 had a mean score of 24.8 with a standard deviation of 4.3, while the 200 students in group 2 had a mean score of 19.5 with a standard deviation of 4.2. Complete parts (a) and (b) below.

 (a) Determine the 90% confidence interval for the difference in scores, μ1- μ2. Interpret the interval.

 The lower bound is _______ 

 The upper bound is _______ 

 (Round to three decimal places as needed.)

 Interpret the interval. Choose the correct answer below.

 OA. There is a 90% probability that the difference of the means is in the interval.

 OB. The researchers are 90% confident that the difference of the means is in the interval.

 OC. The researchers are 90% confident that the difference between randomly selected individuals will be in the interval.

 OD. There is a 90% probability that the difference between randomly selected individuals will be in the interval.

 (b) What does this say about priming?

 OA. Since the 90% confidence interval contains zero, the results suggest that priming does have an effect on scores.

 OB. Since the 90% confidence interval does not contain zero, the results suggest that priming does not have an effect on scores. 

 OC. Since the 90% confidence interval contains zero, the results suggest that priming does not have an effect on scores.

 OD. Since the 90% confidence interval does not contain zero, the results suggest that priming does have an effect on scores.

Answer 1

Q1:

a) Answer C. Discrete. The possible values are x = 0, 1, 2, ....

b) Answer B. Continuous. The possible values are x >= 0

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Q2:

a)

For Sample 1 : x̅1 = 24.8, s1 = 4.3, n1 = 200

For Sample 2 : x̅2 = 19.5, s2 = 4.2, n2 = 200

df = ((s1²/n1 + s2²/n2)²)/[(s1²/n1)²/(n1-1) + (s2²/n2)²/(n2-1) ] = 397.7798 = 398

90% Confidence interval for the difference :

At α = 0.1 and df = 398, two tailed critical value, t_c = T.INV.2T(0.1, 398) = 1.649

Lower Bound = (x̅1 - x̅2) - t_c*√(s1²/n1 +s2²/n2) = (24.8 - 19.5) - 1.649*√(4.3²/200 + 4.2²/200) = 4.599

Upper Bound = (x̅1 - x̅2) + t_c*√(s1²/n1 +s2²/n2) = (24.8 - 19.5) + 1.649*√(4.3²/200 + 4.2²/200) = 6.001

4.599 < µ1 - µ2 < 6.001

Answer B.

b)

Answer: D.