Week 3 Problems

Exercises

In the exercises sections in the chapters, of your textbook, Statistics for Management and Economics, perform the following activities:

"Random Variables and Discrete Probability Distributions": 7.84 and 7.97 "Continuous Probability Distributions": 8.35 and 8.42 "Inference about Comparing two Populations": 13.5 and 13.8 "Chi-Squared Tests": 15.48 and 15.56

Submit your answers in a 4- to 5-page Microsoft Word document and import any associated work in Microsoft Excel.

Cite any sources using the APA format on a separate page.

7.84

Given a binomial random variable with n = 10 and p = .3, use the formula to find the following probabilities.

a. P(X = 3)

b. P(X = 5)

c. P(X = 8)

7.97

In the United States, voters who are neither Democrat nor Republican are called Independents. It is believed that 10% of all voters are Independents. A survey asked 25 people to identify themselves as Democrat, Republican, or Independent.

a. What is the probability that none of the people are Independent?

b. What is the probability that fewer than five people are Independent?

c. What is the probability that more than two people are Independent?

8.35

X is normally distributed with mean 250 and standard deviation 40. What value of X does only the top 15% exceed?

8.42

Travelbyus is an Internet-based travel agency wherein customers can see videos of the cities they plan to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400.

a. What is the probability of getting more than 12,000 hits?

b. What is the probability of getting fewer than 9,000 hits?

13.5

In random samples of 25 from each of two normal populations, we found the following statistics:

x̄1 = 524 s1 = 129

x̄2 = 469 s2 = 141

a. Estimate the difference between the two population means with 95% confidence.

b. Repeat part (a) increasing the standard deviations to s1 = 255 and s2 = 260.

c. Describe what happens when the sample standard deviations get larger.

d. Repeat part (a) with samples of size 100.

e. Discuss the effects of increasing the sample size

Notes for 15.60

If the sample size is less than or equal to 80, we employ the minimum number of intervals, 4. When the sample size is less than 32, at least one expected value will be less than 5. The intervals are

Interval Probability

Z ≤ −1 .1587

−1 < Z ≤ 0 .3413

0 < Z ≤ 1 .3413

Z > 1 .1587

15.60

A random sample of 50 observations yielded the following frequencies for the standardized intervals:

Interval Frequency

Z ≤ −1 6

−1 < Z ≤ 0 27

0 < Z ≤ 1 14

Z > 1 3

Can we infer that the data are not normal? (Use α = .10.)

15.68

Suppose that the personnel department in Exercise 15.42 continued its investigation by categorizing absentees according to the shift on which they worked, as shown in the accompanying table. Is there sufficient evidence at the 10% significance level of a relationship between the days on which employees are absent and the shift on which the employees work?

Day of the Week Monday Tuesday Wednesday Thursday Thursday

Day 52 28 37 31 33

Evening 35 34 34 37 41