Show all your work to receive full credit 1 The local county

Show all your work to receive full credit.

1. The local county is considering a budget proposal that would reallocate funding to renovate the city pools. A survey is conducted to measure public opinion of the proposal. A total of 200 individuals responded to the survey. Fifty of the respondents were from the city and 150 were from the surrounding suburbs. Location Proposal City Suburb Total Favor 39 79 118 Oppose 11 71 82 Total 50 150 200 Is there a relationship between the opinion and the location of the resident at a level of significance of 0.05? 2. A researcher wishes to conduct a study on the self-esteem levels of adolescents. She believes that male adolescents have higher self-esteem than female adolescents. Self-esteem test were administered to 50 randomly selected male and 50 female adolescents. (The maximum score possible was a 10.) Males 1 3 6 5 1 10 8 10 1 9 8 10 5 10 10 2 6 7 7 2 7 8 5 7 6 7 2 3 8 4 10 9 10 2 2 6 2 9 8 9 1 4 4 5 10 6 7 2 10 9 6 9 9 4 2 Females 1 2 2 1 6 4 1 7 6 3 4 3 2 4 5 9 5 2 7 6 5 7 9 4 9 1 4 3 7 8 4 2 6 5 2 4 2 6 4 3 6 9 1 9 3 5 4 9 8 2 8 8 9 7 5 Do the results indicate that self-esteem is significantly higher on average for males at significance level of 0.01? 3. A social researcher believes the color red causes men’s attraction to women to increase as well as women’s attraction to men. The color does not appear to have an effect on same sex attractions. A study was conducted in which photographs of male and female subjects in red and white were shown to participants. They were asked to rate attractiveness of each photograph. Female Male White 5 3 6 5 5 4 3 3 4 6 5 6 3 4 5 6 6 6 3 4 Red 7 7 7 8 5 4 5 6 9 9 10 6 8 9 10 10 4 5 6 6 Use the above information from the study to evaluate the main effects and the interaction at a level of significance of 0.05. Describe the effects of color on the judgments of males and females. (Adapted from Statistics for the Behavioral Sciences by Frederick J Gravetter and Larry B. Wallnau (9th edition), 2013, Wadsworth Cengage Learning)

Solution

We have given that the local county is considering a budget proposal that would reallocate funding to renovate the city pools. A survey is conducted to measure public opinion of the proposal. A total of 200 individuals responded to the survey.

Fifty of the respondents were from the city and

150 were from the surrounding suburbs.

Is there a relationship between the opinion and the location of the resident at a level of significance of 0.05.

alpha = 0.05

The null and alternative hypothesis will be,

H₀ : there is not a relationship between the opinion and the location of theresident

H₁ : there a relationship between the opinion and the location of the resident.

The test statistic for testing is,

² = (O - E)² / E

where O is the observed frequency

E is the expected frequency

E = (Row total) * (column total) / sample size

The observations are,

Location Proposal City Suburb Total Favor 39 79 118

Oppose 11 71 82

Total 50 150 200

The table for observed frequency and expected frequency will be,

² = 9.9490

The critical value for ² is

d.f. = (R-1)(S-1)

where R is number of rows = 2

S is number of columns = 2

d.f.= (2-1)*(2-1) = 1*1 = 1

We find critical value by using EXCEL command,

chiinv (alpha = 0.05 , d.f. = 1)

critical value = 3.841

²  > critical value

Reject H₀ at 5% level of significance.

There a relationship between the opinion and the location of the resident.

2) The hypothesis for the test is,

H₀ : There is no significant difference in the self esteem scores of males and females.

H₁ : There is a significant difference in the self esteem scores of males and females.

alpha = 0.01

Here sample ata is given so we use t-test for the hypothesis.

Here first we check the variances are equal or not.

H₀ : The variances are equal

H₁ : The variances are not equal

The result for this is as follows,

The summary statistic is,

  

And the test statistic for variance and two sample mean will be,

d.f. = n1 + n2 - 2 = 55 +55 -2 = 108

F = 2.522

p-value = 0.00044

p-value < 0.01

reject H₀ at 1% level of significance.

The variances are not equal.

So we use unpooled variance.

s² = (s1² / n1) + (s2² / n2)

p-value is 0.030

p-value > 0.01

Fail to reject H₀ at 1% level of significance.

There is no significant difference in the self esteem scores of males and females.

proposal	location	suburbs	total
favor	39	79	118
oppose	11	71	82
total	50	150	200