Question 10 please Find the sample mean. Draw a graph of the empirical distribut

ID: 3129573 • Letter: Q

Question

Question 10 please

Find the sample mean. Draw a graph of the empirical distribution function (Definition 12.1). Find the sample interquartile range. Compare these values with the population mean, the distribution function (Definition 1.3.4), and the population interquartile range, respectively. If the null hypothesis is true, each customer is equally likely to select the red box or the blue box of cereal. If the alternative hypothesis is true, customers prefer the blue box 3 to 1 over the red box. Assume each customer selects one box of cereal, independently of the other customers. The null hypothesis will be rejected if 15 or more of the first 20 customers select blue boxes. Find the level of significance. Find the power. If 17 of the first 20 customers actually observed selected blue boxes, find the p-value. Seven male students have interviewed for three positions as summer camp counselors, the students are ranked according to height, from 1 (tallest) to 7 (shortest). The null hypothesis is that each student is equally likely to be selected, while the alternative hypothesis it that the three taller students are twice as likely to be selected as the four shorter students. Assume the student are selected independently of each other. The test

Explanation / Answer

Question 10

Solution:

Here, we have to calculate the level of significance and power of the test for the given scenario. We are given the following information:

Customers prefer blue boxes 3 to 1 over red boxes.

Power of test = 1/(3+1) = ¼ = 0.25

Hypothesis will be rejected if 15 or more customers out of 20 customers select blue box.

The level of significance = alpha value = 15/20 = 0.75 or 75%

Now, we have to find the p-value for the test in which 17 customers out of 20 customers select blue boxes.

For finding the p-value, we have to use the one sample z test for proportion which is given as below:

Z Test of Hypothesis for the Proportion

Data

Null Hypothesis p =

0.75

Level of Significance

0.25

Number of Items of Interest

Sample Size

Intermediate Calculations

Sample Proportion

0.85

Standard Error

0.0968

Z Test Statistic

1.0328

Two-Tail Test

Lower Critical Value

-1.1503

Upper Critical Value

1.1503

p-Value

0.3017

Do not reject the null hypothesis