One, Two-Sample Tests of Hypothesis, Variance,and Chi-square

One, Two-Sample Tests of Hypothesis, Variance, and Chi-squared Analysis

Exercises 19 and 20 (Ch. 17)

19. In a particular market there are three commercial television stations, each with its own
evening news program from 6:00 to 6:30 P.M. According to a report in this morning's local
newspaper, a random sample of 150 viewers last night revealed 53 watched the news
on WNAE (channel 5), 64 watched on WRRN (channel 11), and 33 on WSPD (channel 13).
At the .05 significance level, is there a difference in the proportion of viewers watching
the three channels?

20. There are four entrances to the Government Center Building in downtown Philadelphia.
The building maintenance supervisor would like to know if the entrances are equally utilized.
To investigate, 400 people were observed entering the building. The number using
each entrance is reported below. At the .01 significance level, is there a difference in the
use of the four entrances?

Entrance Frequency
Main Street 140
Broad Street 120
Cherry Street 90
Walnut Street 50
Total 400

Solution Summary

Complete, Neat and Step-by-step Solutions are provided in the attached file.

What are the four assumptions for the chi-squaretests?
What are the hypothesis when conducting the chi-squaretests for goodness-of-fit?
Why is there just one critical value for a chi-square test even when the hypothesis is a two-tailed test?

A chi-square test statistic was calculated to be 18, based on a sample variance of 20 and a hypothesized population variance of 40. How many observations were made when the sample was extracted? Which one?
a. 9
b. 10
c. 36
d. 37

Suppose that on a 100-point test, the goal is for the students' exam scores to have a standard deviation of less than 10 pts. A recent sample of 22 exams has a standard deviation of 12.1. Use alpha = 0.05.
H0: population variance > or = 100
H1: population variance < 100
What is the critical Chi-square value?
For the same

The filling weight for boxes of cereal is designed to have a variance .02 ounces or less. A sample of 41 boxes of cereal shows a sample standard deviation of .16 ounces. Use alpha = .05 to determine whether the variance in the cereal box filling weight is exceeding the design specification.

1. Why do the critical values from the Chi-square distribution get larger as the degrees of freedom get larger? Recall that this is opposite the pattern for the t-table.
2. Why is choosing sample size important(with specific reference to proportions)?

The TMC Daily News reported that the color distribution for plain N&N'S was: 40%brown, 20%yellow 20% orange, 10% green, and 10% tan. Each piece of candy in a random sample of 100 plain N&N'S was classified according to color, and the results are listed low. Use a 0.05 significance level to test the claim that the published color

I am having trouble completing this problem. I know what it is asking for but calculating it has me completely stuck. Please help!!!!
Exam scores of 40 students in a statistics class are shown. (a) Estimate the mean and standard deviation from the sample. (b) Assuming that the data are from a normal distribution, define bin

3. A survey of 30 students at a local college found that the sample mean number of hours worked by students is 17 hours per week with a sample standard deviation of 2 hours. Use a 0.05 significance level to test the claim that the sample students come from a population with a standard deviation of 3 hours. (Assume that the sa

A random sample of 51 observations was selected from a normally distributed population. The sample mean was xbar = 88.6, and the sample variance was s2 = 38.2. Does the sample show sufficient reason to conclude that the population standard deviation is not equal to 8 at the 0.05 level of significance? Use the p-value method.

ANOVA (Analysis of Variance), One-way ANOVA F-test, & Chi-Square test
Q1: What are some real life examples of the use of Chi-Squaretests using contingency tables?
Q2: Why is a test, which is testing significant differences among means called Analysis of Variance?
Q3: Why might a non-parametric test be used, in plac