# Statistics - Hypothesis Testings of Relationships

See the attached file.

Problem #1

A total of 200 people in each of three grocery stores were asked if they favored, opposed,

or were indifferent to the sale of lottery tickets in grocery stores. The results of the survey

are summarized below. Test the hypothesis at α= 0.05.

Opinion Store A Store B Store C

Favor 21 78 94

Oppose 101 63 27

Indifferent 78 59 79

Problem #2

A professor of economics wants to study the relationship between income (y in $1000s) and education (x in years). A random sample eight individuals is taken and the results are shown below.

Education 16 11 15 8 12 10 13 14

Income 58 40 55 35 43 41 52 49

Test to see if there is any significant relationship between income and education. Use α = .05.

Problem #3

Thirty-five employees who completed two years of college were asked to take a basic mathematics test. The mean and standard deviation of their scores were 75.1 and 12.8, respectively. In a random sample of 50 employees who only completed high school, the mean and standard deviation of the test scores were 72.1 and 14.6, respectively.

a. Can we infer at the 10% significance level that a difference exists between the two groups?

b. Estimate with 90% confidence the difference in mean scores between the two groups of employees. Explain how to use this interval estimate to test the hypotheses.

#### Solution Preview

Please see the attached file.

Problem #1

A total of 200 people in each of three grocery stores were asked if they favored, opposed,

or were indifferent to the sale of lottery tickets in grocery stores. The results of the survey

are summarized below. Test the hypothesis at α= 0.05.

Opinion Store A Store B Store C

Favor 21 78 94

Oppose 101 63 27

Indifferent 78 59 79

Answer

The null hypothesis tested is

H0: There is no significant difference in the proportion of opinion in the three stores.

The alternative hypothesis is

H1: There is significant difference in the proportion of opinion in the three stores.

The test statistic used is

The test statistic used is

where

O - Observed frequency

E - Expected frequency

The expected frequencies are calculated assuming that the null hypothesis is true.The Expected frequencies are given below. They are calculated using the formula , ,where Ri , ith row total, Cj jth column total and G is the grand Total.

Rejection criteria: Reject the null hypothesis if the calculated value of Chi square is greater than the critical value of chi square with 4 d.f

Details

The expected frequencies are given below

Opinion Store A Store B Store C

Favor 64.33333 64.33333 64.33333

Oppose 63.66667 63.66667 63.66667

Indifferent 72 72 72

The Chi square contribution from each cell is

Opinion Store A Store B Store ...

#### Solution Summary

A total of 200 people in each of three grocery stores were asked if they favored, opposed,