Children in the United States account directly for $ 36 billion in sales annuall
ID: 1241713 • Letter: C
Question
Children in the United States account directly for $ 36 billion in sales annually. When their indirect influence over product decisions is considered, the total economic spending affected by children in the US is $ 290 billion. It is estimated that by age 10, a child makes an average of more than 5 trips per week to a store. Suppose that you want to prove that children in Los Angeles average more than 5 trips a week to a store. Let represent the population mean number of times children in Los Angeles make trips to a store.a) State the null and the alternative hypotheses.
b) Explain the meaning of the Type I and Type II errors in the context of this scenario.
c) In Los Angeles, you take a sample of 100 children and find that the mean number of trips to the store is 5.47 and the sample standard deviation of the number of trips to the store is 1.6. At the 0.01 level of significance, is there evidence that the population mean number of trips to the store is greater than 5 per week?
Explanation / Answer
a) The null hypothesis is H0: µ = 5 The alternative hypothesis is Ha: µ > 5 b) A Type I error would occur if we were to reject the null hypothesis and conclude that the average number of trips to the store was greater than 5 per week when, in fact, the average is actually less than or equal to 5. A Type II error would occur if we were to fail to reject the null hypothesis, and conclude that there was not sufficient evidence to support the claim that the average number of trips to the store was greater than 5 per week when, in fact, the average actually is greater than 5. c) The test statistic is (5.47 - 5.00) / (1.6 / v100) = 2.9375. The p-value corresponding to z = 2.9375 is 0.0017 Since the p-value (0.0017) is less than the level of significance (0.01), the decision would be to reject the null hypothesis, and conclude that there is sufficient evidence to support the claim that the average number of trips to the store is greater than 5 per week.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.