1. In the popular 2004 movie Sideways, the main character\'s favorite wine was P

Question

1. In the popular 2004 movie Sideways, the main character's favorite wine was Pinot Noir and he refused to drink a red wine called Merlot. After the movie was in theaters for a couple months, several surveys of Napa Valley wine-tasting customers' red wine preferences were conducted. The results were: 42% preferred Pinot Noir, 24% preferred Cabernet Sauvignon, 20% preferred Syrah, 8% preferred Merlot, and 6% preferred other varietals. Last year, in a survey of 200 randomly selected Napa Valley wine-tasting customers: 67 preferred Pinot Noir, 66 preferred Cabernet Sauvignon, 38 preferred Syrah 15 preferred Merlot, 14 preferred Other varietals. This data was tested using a chi-square goodness of fit test. The results are shown below Chi-Square Goodness-of-Fit Test for Observed Counts in Variable: Counts Using category names in Wines Contribution to Chi-Sq 3.44048 6.75000 0.10000 0.06250 0.33333 Test Observed Proportion Expected 84 48 40 16 12 Category Pinot Noir Cabernet Sauvignon 67 38 15 14 0.42 0.24 0.20 0.08 0.06 Merlot Other N DF Chi-Sq P-Value 0.030 2004 10.6863 Based on the above test results, which of the following is/are true? A. At the 5% level, we have significant evidence that the 2004 preferences have not changed. B. At the 5% level, we have significant evidence that the 2004 preferences have changed. C. At the 5% level, there appears to be a significant switch of Pinot Noir drinkers to Cabernet Sauvignon. D. Both B and C. E. Both A and C

Explanation / Answer

Question 1

Answer: B. At the 5% level, we have significant evidence that the 2004 preferences have changed.

Explanation: For the given chi square test of goodness of fit, we get the p-value 0.030 which is less than given level of significance or alpha value 0.05, so we reject the null hypothesis that the 2004 preferences are not changed. This means, there is sufficient evidence to conclude that 2004 preferences have changed.

Question 2

Part a

The null and alternative hypotheses for the given F test are summarized as below:

Null hypothesis: H0: Population standard deviation for sample 1 and sample 2 are same.

Alternative hypothesis: Ha: Population standard deviation for sample 1 is greater than the population standard deviation for sample 2.

This is a one tailed test. This is an upper tailed test.

Part b

The test statistic formula is given as below:

F = S1^2/S2^2

We are given S1 = 9.9 and S2 = 6.6

N1 = 16 and N2 = 22

DF1 = 16 – 1 = 15 and DF2 = 22 – 1 = 21

F = 9.9^2/6.6^2 = 98.01/43.56 = 2.25

Test statistic = F = 2.25

Part c

We are given S1 = 9.9 and S2 = 6.6

N1 = 16 and N2 = 22

DF1 = 16 – 1 = 15 and DF2 = 22 – 1 = 21

= 0.10

Critical value = 1.8271

(By using F-table or excel)

P-value = 0.0432

(By using F-table or excel)

P-value < = 0.10

So, we reject the null hypothesis that Population standard deviation for sample 1 and sample 2 are same.

There is sufficient evidence to conclude that Population standard deviation for sample 1 is greater than the population standard deviation for sample 2.

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