Question

4. A market analysis wishes to see whether consumers have any preference between five different flavors of chewing gum. A sample of 100 people provided the data below. Does enough evidence exist to reject the claim that no preference exists in the selection of chewing gum flavors? (10 points) Observed Expected 32 20 28 20 Frequency Mint Bubble Gum Strawberry Grape Orange 16 20 14 20 10 20 5. A medical researcher wishes to see whether the variance of the heart rates (in beats per minute) of smokers is different from the variance of heart rates of people who do not smoke. Below is the data from two samples. Using a = 0.05, is there enough evidence to support the claim? (10 points) Smokers Non-Smokers ni = 26 nz= 18 512 = 32 $22 = 10 6. Discuss in general the use of the Sign Test for Matched Pairs, Rank-Sum Test and the Spearman Rank Correlation Test. (10 points)

Answer 1

4)

Null hypothesis:

The consumers have preference between five different flavors of chewing gum.

Alternative hypothesis:

The consumers don’t have preference between five different flavors of chewing gum.

test statistic is

χ =Σ (Ο-Ε)' Ε, (32 – 20) (28 – 20) (16–20) (14 – 20)(10 – 20) 20 20 20 20 20 = 7.2 +3.2 + 0.8+1.8+5 =18

Based on the information provided, the significance level is a = 0.05, the number of degrees of freedom is df = 5 – 1= 4, so then the rejection region for this test is R= {x? : x² > 9.488}.

Since it is observed that y’ = 18 > xě = 9.488, it is then concluded that the null hypothesis is rejected.

Hence we conclude that The consumers don’t have preference between five different flavors of chewing gum.

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