1. A fine dining restaurant claims that the group sizes of their customers follows the following distribution:

2 people	3 people	4 people	4+ people
38%	10%	17%	35%

Gustavo, a waiter at the restaurant, would like to test this claim. He takes a sample of 88 customers and records the observed frequencies in the following table:

2 people	3 people	4 people	4+ people
40	0	24	24

(a) In performing this statistical test, state the hypotheses.

• H₀: the proportions of customers for each group are all the same vs. H_A: the proportions of customers for each group are not all the same

• H₀: the distribution of customers for each group is the same as the observed frequencies vs. H_A: the distribution of customers for each group is not the same as the observed frequencies

• H₀: the distribution of customers for each group is not the same as claimed by the restaurant vs. H_A: the distribution of customers for each group is the same as claimed by the restaurant

• H₀: the distribution of customers for each group is the same as claimed by the restaurant vs. H_A: the distribution of customers for each group is not the same as claimed by the restaurant

• H₀: the distribution of customers for each group is not the same as the observed frequencies vs. H_A: the distribution of customers for each group is the same as the observed frequencies

(b) What is the expected frequencies of each group? Fill out the table. (Round your answers to 2 decimal places, if needed.)

2 people	3 people	4 people	4+ people

(c) What is the test statistic value for this hypothesis test? (Round your answers to 2 decimal places, if needed.) TS = _________

(d) The test statistic follows a _________ (t-distribution with df = 3 / chi-square distribution with df = 4 / t-distribution with df = 4 / chi-square distribution with df = 87 / chi-square distribution with df = 3.)

(e) Using the statistical table, the p-value is _________ (0.05 < p-value < 0.10 / 0.01 < p-value < 0.025 / 0.025 < p-value < 0.05 / p-value > 0.10 / 0 < p-value < 0.005 / 0.005 < p-value < 0.01 .)

(f) Based on the p-value, those conducting the test should _________ (reject fail to reject) the null hypothesis at the significance level of 0.025.

(g) What is the appropriate conclusion?

• There is sufficient evidence to conclude the distribution of customers for each group is not the same as claimed by the restaurant.

• There is sufficient evidence to conclude the proportions of customers for each group are not all the same.

• There is sufficient evidence to conclude the distribution of customers for each group is the same as claimed by the restaurant.

• There is insufficient evidence to conclude the distribution of customers for each group is not the same as claimed by the restaurant.

• There is insufficient evidence to conclude the proportions of customers for each group are not all the same.

2. Mitchell works in the produce section at a small local supermarket and would like to test whether the proportion of apples people purchase is the same for each season, using a significance level of 0.05. He analyzes the apple purchases each season for a year and records his findings in the following table.

Season	Spring	Summer	Fall	Winter	Total
# of apples purchased	1181	1134	1134	1274	4723

(a) In performing this statistical test, state the hypotheses.

• H₀: the distribution of apples people purchased is the same for each season vs. H_A: the distribution of apples people purchased is not the same for each season

• H₀: the distribution of apples people purchased is not the same for each season vs. H_A: the distribution of apples people purchased is the same for each season

• H₀: the proportion of customers is the same each season vs. H_A: the proportion of customers is not the same each season

• H₀: the total number of apples people purchased is not the same for each season vs. H_A: the total number of apples people purchased is the same for each season

• H₀: the observed number of apples people purchased is the same for each season vs. H_A: the observed number of apples people purchased is not the same for each season

(b) What is the expected number of apples purchased for each season? Fill out the table. (Round your answers to 2 decimal places, if needed.)

Spring	Summer	Fall	Winter

(c) What is the test statistic value for this hypothesis test? (Round your answers to 2 decimal places, if needed.) TS = _________

(d) The test statistic follows a _________ (chi-square distribution with df = 3 / t-distribution with df = 3 / chi-square distribution with df = 4 / t-distribution with df = 4 / chi-square distribution with df = 4722.) (e) Using the statistical table, the p-value is _________ (0.025 < p-value < 0.05 / 0 < p-value < 0.005 p-value > 0.10 / 0.005 < p-value < 0.01 / 0.01 < p-value < 0.025 / 0.05 < p-value < 0.10 .) (f) Based on the p-value, those conducting the test should _________ (reject / fail to reject) the null hypothesis at the significance level of 0.05. (g) What is the appropriate conclusion?

• There is insufficient evidence to conclude the total number of customers for each season are not all the same.

• There is sufficient evidence to conclude the total number of customers for each season are not all the same.

• There is insufficient evidence to conclude the distribution of apples purchased is not the same for each season.

• There is sufficient evidence to conclude the distribution of apples purchased is not the same for each season.

• There is sufficient evidence to conclude the distribution of customers apples purchased is the same for each season.

3. Random samples of 53 male students and 56 female students at the U of A were asked to state their car preference (American, European, and Japanese). The resulting frequencies are shown in the following table. Is there enough evidence to conclude a difference in car preference between males and females?

	American	European	Japanese
Male	20	12	21
Female	15	25	16

(a) In performing this statistical test, state the hypotheses.

• H₀: the proportion of males is the same for each car preference vs. H_A: the proportion of males is not the same for each car preference

• H₀: the proportion of females is the same for each car preference vs. H_A: the proportion of females is not the same for each car preference

• H₀: the distribution of preference is the same for males and females vs. H_A: the distribution of preference is not the same for males and females

• H₀: the distribution of preference is not the same for males and females vs. H_A: the distribution of preference is the same for males and females

• H₀: the distribution of gender is not the same for each car preference vs. H_A: the distribution of gender is the same for each car preference

(b) What is the expected frequencies of each cell? Fill out the table. (Round your answers to 2 decimal places, if needed.)

	American	European	Japanese
Male	17.02
Female			19.01

(c) What is the test statistic value for this hypothesis test? (Round your answers to 2 decimal places, if needed.) TS = _________ (d) The test statistic follows a _________ (chi-square distribution with df = 107 / t-distribution with df = 2 / chi-square distribution with df = 2 / t-distribution with df = 6 / chi-square distribution with df = 6.) (e) Using the statistical table, the p-value is _________ (0.025 < p-value < 0.05 / 0.01 < p-value < 0.025 / 0 < p-value < 0.005 / 0.005 < p-value < 0.01 / p-value > 0.10 / 0.05 < p-value < 0.10 .) (f) Based on the p-value, those conducting the test should _________ (fail to reject / reject) the null hypothesis at the significance level of 0.025. (g) What is the appropriate conclusion?

• There is sufficient evidence to conclude there is a difference in males and females for car preference.

• There is insufficient evidence to conclude the proportion of males is not the same for each car preference.

• There is sufficient evidence to conclude the proportion of males is not the same for each car preference.

• There is insufficient evidence to conclude there is a difference in males and females for car preference.

• There is sufficient evidence to conclude there is no difference in males and females for car preference.

4. Olivia attends school at the University of Alberta and decides to compile a contingency table of students who are taking various degrees. She surveys a group of students, and the data she collects is listed in the contingency table below. Olivia want to see if degree and gender are dependent variables.

	PhD	Masters	Undergraduate
Male	18	21	79
Female	11	26	67

(a) In performing this statistical test, state the hypotheses.

• H₀: Degree is related to gender vs. H_A: Degree is not related to gender

• H₀: The proportion of female students is the same as the proportion of male students vs. H_A: The proportion of female students is not the same as the proportion of male students

• H₀: Degree and gender are dependent vs. H_A: Degree and gender are independent

• H₀: Degree and gender are independent vs. H_A: Degree and gender are dependent

• H₀: Degree is associated with gender vs. H_A: Degree is not associated with gender

(b) What is the expected frequencies of each cell? Fill out the table. (Round your answers to 2 decimal places, if needed.)

	PhD	Masters	Undergraduate
Male	15.41
Female			68.4

(c) What is the test statistic value for this hypothesis test? (Round your answers to 2 decimal places, if needed.) TS = _________

(d) The test statistic follows a _________ (chi-square distribution with df = 220 /chi-square distribution with df = 6 / t-distribution with df = 6 / t-distribution with df = 2 / chi-square distribution with df = 2.)

(e) Using the statistical table, the p-value is _________ (0.025 < p-value < 0.05 / 0 < p-value < 0.005 / 0.01 < p-value < 0.025 / 0.005 < p-value < 0.01 / 0.05 < p-value < 0.10 / p-value > 0.10 .)

(f) Based on the p-value, those conducting the test should _________ (fail to reject / reject) the null hypothesis at the significance level of 0.05.

(g) What is the appropriate conclusion?

• There is sufficient evidence to conclude degree and gender are independent.

• There is sufficient evidence to conclude degree and gender are dependent.

• There is insufficient evidence to conclude degree and gender are dependent.

• There is sufficient evidence to conclude the proportion of females is not the same for each degree.

• There is insufficient evidence to conclude degree and gender are independent