9.38 Taste Testing In a head-to-head taste test of store-brand foods versus nati
ID: 3134110 • Letter: 9
Question
9.38 Taste Testing In a head-to-head taste test of store-brand foods versus national brands, Consumer Reports found that it was hard to find a taste difference in the two 12 If the national brand is indeed better tast- ing than the store brand, it should be judged as better more than 50% of the time. a. State the null and alternative hypothesis to be tested. Is this a one- or a two-tailed test? b. Suppose that, of the 35 food categories used for the taste test, the national brand was found to be better than the store brand in 8 of the taste comparisons. Use this information to test the hypothesis in part a. Use a 0.01. What practical conclusions can you draw from the results?Explanation / Answer
a)
Let p = the population proportion who like the national brand.
By default, we set the null hypothesis to have the national brands to be better.
Ho: p >= 0.50
Ha: p < 0.50 [ANSWER]
This is a one tailed test. [ANSWER]
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b)
Formulating the null and alternative hypotheses,
Ho: p >= 0.5
Ha: p < 0.5
As we see, the hypothesized po = 0.5
Getting the point estimate of p, p^,
p^ = x / n = 0.228571429
Getting the standard error of p^, sp,
sp = sqrt[po (1 - po)/n] = 0.084515425
Getting the z statistic,
z = (p^ - po)/sp = -3.211586168
As this is a 1 tailed test, then, getting the p value,
p = 0.000660022
significance level = 0.01
As P < 0.01, we REJECT THE NULL HYPOTHESIS.
Hence, there is significant evidence that the store brands are better than the national brands at 0.01 level. [CONCLUSION]
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