Chi-Square Test; - ANOVA; (D)

Chi-square test; - ANOVA; (d) z-Test

Perform a chi-square test on the following data:

Regulation is the best way to ensure a safe workplace

To compute for expected values:

Expected value= [(row total of a/row, col totals of AB) (row total of B/row, col totals of AB)] [row, col totals of AB]

O EOE Total (Row) Managers 58-62 34-29 8-4 100 Blue-collar workers 66-62 24-29-10 9 100 Total (Column) 124 58-18-200 *O- observed; E-expected

To calculate for X2:

X2= ? (Observed-Expected) 2/Expected)

Managers

Blue-collar workers

Ownership of residence

Total (Row)

Male

Female

Total (Column)

O- observed; E-expected

Male

Female

Age of shopper

& over OE Total (Row) Store a 27-22 31-24.6-11-22.6-69 Store B. 73-78 82-88.4-93-81.4 248 Total (Column) 100-113 104-317 *O- observed; E-expected

& over Store a Store B

X2= 1.26 + 0.35 + 1.67 + 0.46 + 5.98 + 1.66 = 11.39

Collapsed response categories:

Grade school: Less than grade 8

High school: Some high school, High school graduate

College: Some college, College graduate

Post-graduate: Master's degree, Ph.D. degree

Combined observed and expected frequencies using the collapsed categories

Grade school

High school

Post-graduate

O EOE Total (Row) Owners 0-3.6-35-31.2-22-21.7-5-5.4-62 Nonowners 8-4.4-34-37.8-26-26.3-7-6.6-75 Total (Column) 8-69-48 12-137 *O- observed; E-expected

Grade school

High school

Post-graduate

Owners

Nonowners

X2= 3.62 + 2.99 + 0.46 + 0.38 + 0.03 + 0.03 = 7.52

In the table illustrated below, the given data are shown and proportionate percentage computations for the sample were generated (based on frequencies given). The table highlights that the sample generated for each employment category is not representative of the population. In fact, the sample is overestimated for full-time employees, the sample having a 10% difference from the population percentage. Part-time and laid-off employees, meanwhile, are under-represented. Part-time employees are under-represented by 8%, while laid-off employees are under-represented by 2%. In addition to the under- and over-representation of the sample sizes per category, the sample size itself plays a big role in increasing the chances that this sample is not representative of the population. In this case, sample size is only n=50, a statistically readable, although still a small sample to be considered representative of the population. Representativeness becomes more probable as the sample size increases.

Population

Sample

Full-time

Part-time

Laid-off

To further support this observation, standard error of the sample is also computed, determining if indeed, as posited earlier, the sample is not representative of the population under study. The following is the formula for the standard error:

Standard error = ?[? (score in distribution-sample mean) 2] - [n-1]

529)+(121)+(169)] - 49 = ?819-49 = ?770 = 27.75

The standard value of 27.75 represents the distance of each score or frequency of representation of each employment category to the average or mean score or frequency for the distribution (i.e., employment categories.

Looking at the gender-commuting relationship, a possible hypotheses that can be developed from these variables are the following:

Ho: There is no significant relationship between commuting and gender.

H1: There is a significant relationship between commuting and gender.

SPSS results showed that generally, respondents went to work by driving a car. Directionally, females are more likely to take the passenger train (73%), while more than the majority of male respondents work at home (62%). However, these findings are not significant, and the X2 asymp. sig value of 0.101 showed that p< 0.05, which means that Ho is retained -- that is, there is no significant relationship between commuting and gender.

To determine the significance of the relationship between the variables savings and loans and other financiers, an independent samples t-test will be conducted as the statistical analysis. The null hypothesis for this analysis is:

Ho: There is no significant difference between savings and loans and other financiers in the average payback period necessary to justify solar heating systems for residences.

To conduct the t-test, the following formula will be used:

observed difference between sample means / standard error of the difference between means

X1-X2 / S (x1-x2) where: S (x1-x2) = ?sx12 + sx22

Applying the given data to the formula above, we get:

Savings & Loans

Other Financiers

Sample mean

Standard error

S (x1-x2)

Sample size df (n1 + n2 -2)

(8.7-7.7) / 1.05 = 1 / 1.05 = 0.95

At t=0.95 and df=162, the difference between the sample of savings and loans and sample of other financiers represents no real difference between the larger population of these two variables/groups. Thus, null hypothesis is retained.