Study

Attaining our sample

The population of interest in this case was the students of North Olmsted High School. We determined that the best sample size for this would be 100 students. Originally, we intended to have 50 males and 50 females, but it would have taken too long and not really affect the results when using the Minitab output to generate the sample. A list of all the students at the high school, stored in an Excel file, was imported to Minitab under 'Surname' and 'First Name' columns. Using Minitab's random generator, 100 students were randomly selected and placed in column C1 and C2. The list was alphabetized by first and last name. After obtaining this sample, surveys were sent to the students based on when their study halls were scheduled.

The following is an example of what was asked in our survey.

1. Gender: Male   Female

2. Which ice cream flavor do you prefer of the following types?     Chocolate     Vanilla

R e s u l t s

Chi-Square Test: Chocolate, Vanilla

Ho: There is no association between ice cream flavor preference and flavor.

Ha: There is an association between ice cream flavor preference and flavor.

Level of significance = 0.05

Assumptions: expected cell counts must be five or greater; the sample used must be random and independently selected.

The formula for the computation of the chi-square test statistic is the sum of the quantity (expected cell count-observed cell count)^2/(expected cell count).

Expected counts are printed below observed counts

Chi-Square contributions are printed below expected counts

       Chocolate  Vanilla  Total

    1         13       22     35

           15.84    19.16

           0.510    0.422

 

    2         30       30     60

           27.16    32.84

           0.297    0.246

 

Total         43       52     95

Chi-Sq = 1.475, DF = 1, P-Value = 0.225

Conclusion: We failed to reject the null hypothesis at 0.05 level of significance because our p-value of 0.225 was greater than alpha. Therefore, we do not have sufficient evidence to suggest that is an association between favorite ice cream flavor and gender.

Test and CI for Two Proportions

π₁: The true proportion of females who prefer vanilla ice cream.

π₂: The true proportion of males who prefer vanilla ice cream.

Ho: π₁ -  π₂ = 0

Ha:  π₁ - π₂ < 0

Level of significance = 0.05

Assumptions: n × p > 10; n × (1 - p) > 10; the data is normally distributed; the samples are randomly and independently chosen.

The z value equals proportion one - proportion two/the square root of proportion one times one minus proportion one / sample size one + proportion two times one minus proportion two / sample size two

Sample   X   N  Sample p

1       13  35  0.371429

2       30  60  0.500000

Difference = p (1) - p (2Estimate for difference:  -0.128571

95% upper bound for difference:  0.0426611

Test for difference = 0 (vs < 0):  Z = -1.24  P-Value = 0.108

 

Fisher's exact test: P-Value = 0.158

Chart of Chocolate, Vanilla

Conclusion: We failed to reject the null hypothesis at 0.05 level of significance since our p-value of 0.108 was greater than alpha. Therefore, we do not have sufficient evidence to suggest that π₁- π₂ < 0.