Frito-Lay Targets the Hispanic Market For questions 1a, 1b, and 2b fill in the c

Question

Frito-Lay Targets the Hispanic Market

For questions 1a, 1b, and 2b fill in the chart. (each seperately)

Many proportions were generated in the focus groups and 1. market research that were conducted for this project, including the proportion of the market that is Hispanic, the proportion of Hispanic grocery shoppers that are women, the proportion of chip purchasers that are teens, and so on Use techniques presented in this chapter to analyze each of the following and discuss how the results might affect marketing decision makers regarding the Hispanic market. a. Suppose that in the past, 94% of all Hispanic grocery shoppers were women. Perhaps due to changing cul- tural values, we believe that more Hispanic men are now grocery shopping. We randomly sample 689 Hispanic grocery shoppers from around the United States and 606 are women. Does this result provide enough evidence to conclude that a lower proportion of Hispanic grocery shoppers now are women? b. What proportion of Hispanics listen primarily to advertisements in Spanish? Suppose one source says that in the past the proportion has been about .83. We want to test to determine whether this figure is true. A random sample of 438 Hispanics is selected, and the Minitab results of testing this hypothesis are shown here. Discuss and explain this output and the implica tions of this study using a 05

Explanation / Answer

Q1Part (a)

Let X = number of Hispanic women grocery shoppers. Then, X ~ B(n, p) where n = sample size and p = probability (which is the same as population proportion) that a grocery shopper is a woman.

Null hypothesis: H0 : p = 0.94    Vs Alternative: HA : p < 0.94

[Rationale: we are given that in the past p was 94%, i.e., 0.94 and we are trying to find if it has come down.]

Test statistic: Z = (x – np)/sqrt{np(1 - p)} where x = number of Hispanic women grocery shoppers in the sample of size n = 689.

So, Z = {606 – (689 x 0.94)}/sqrt(689 x 0.94 x 0.06) = - 41.66/sqrt38.8596 = - 41.66/6.234

So, Z = - 6.683

Distribution

Under H0 probability distribution of above Z can be approximated by Standard Normal Distribution provided both np and npq are greater than 10, which is satisfied in the present case.

Decision criterion: reject H0 if Zcal < Zcrit, where Zcal is the calculated value of the test statistic and Zcrit is the lower % point of Standard Normal Distribution.

Since is not specified in the question, we will take it as 5% (the most frequently used level of significance).

Zcrit, from tables, is – 1.645.

Inference

Since - 6.683 < - 1.645, H0 is rejected.

Conclusion

There is enough evidence to suggest that proportion of Hispanic women grocery shoppers

has come down.

DONE

Q1 Part (b)

Let Y = number of Hispanics who listen primarily to advertisements in Spanish. Then,

Y ~ B(n, p) where n = sample size and p = probability (which is the same as population proportion) that a Hispanic listens to advertisements in Spanish.

Null hypothesis: H0 : p = 0.83    Vs Alternative: HA : p 0.83

[Rationale: we are given that in the past p was 0.83 and we are trying to find if it is true now.]

Test statistic: Z = (y – np)/sqrt{np(1 - p)}where y = number of Hispanics who listen to advertisements in Spanish.n the sample of size n = 438.

Since value of y has been missed out in the question provided(Minitab results), we will complete the exercise with just y.

So, Z = {y – (438 x 0.83)}/sqrt(438 x 0.83 x 0.17) = (y – 363.54)/sqrt61.8018

= (y – 363.54) /7.861

So, Z = (y – 363.54) /7.861

Distribution

Under H0 probability distribution of above Z can be approximated by Standard Normal Distribution provided both np and npq are greater than 10, which is satisfied in the present case.

Decision criterion: reject H0 if | Zcal | > Zcrit, where Zcal is the calculated value of the test statistic and Zcrit is the lower (/2)% point of Standard Normal Distribution.

Since is specified in the question as 5% Zcrit, from tables, is 1.96.

Inference and Conclusion cannot be completed unless the value of y is known.

DONE

[by reverse calculation, H0 will be rejected if y > 376.43 or y < 350.648]

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