For each of the following, state the null and alternative hypotheses, the Type I
ID: 3248264 • Letter: F
Question
For each of the following, state the null and alternative hypotheses, the Type I and Type II errors associated with the hypotheses, and the consequences of each error. A. The decision to implement changes in the current math program at a junior high in Bigcity will be based on a sample of students' scores on a standardized math exam. If the average is less than the statewide average of 89, all math teachers will have to participate in a workshop to revise the curriculum. B. Expensive Clothing, Inc. thinks it had a good year and wants to reward its customers. In a typical year, sales are $75 per customer. If a random sample o this year's sales indicate a better than average year (average sales per customer are higher than $75), a $10 coupon will be given out for two weeks to each customer who spends at least $75. C. Too Many Pets, a pet store, is concerned about its dogs. The store has enough supplies on hand to maintain an estimated in store average of 10 dogs a day. The store wants to know whether its average dog population is actually 10 a day or some other number. If their original estimate is incorrect the store will have to invest in research to determine the actual average and decide how to accommodate the change. Use this scenario to answer the following questions. Colored Wax & Co. sells candles with a mean burn time of 50 minutes. The company wants to test its candles' burn time against a competitor's candles. Researchers from Colored Wax & Co. randomly select 25 candles from its competitor for testing. From previous research, the staff of Colored Wax & Co. knows that sigma = 12.5. A. Colored Wax & Co. wants to test a two-sided alternative hypothesis with a = .05. What are the null and alternative hypotheses for this test? B. What's the probability of a Type I error in this test? C. Describe a Type I error for H_0: mu = 50. D. What is the rejection region (for what values of x will H_0 be rejected) for H_0: mu - 50? E. Describe a Type II error for H_0: mu = 50. F. Suppose the mean burn time is actually 53 minutes. Find the possibility of a Type II error (beta) and the power of the test.Explanation / Answer
Question 1
Answers
A.
Null hypothesis:
H0: 89
Alternative hypothesis:
H1: < 89
In this context, type I error is the event of concluding that the average score on the standardized math score of students is less than the stated average, when actually it is not less than the stated average.
The consequence of type I error is that all math teachers will have to participate in the workshop unnecessarily to revise the curriculum and thereby incur unwanted cost of conducting the workshop.
In this context, type II error is the event of concluding that the average score on the standardized math score of students is not less than the stated average, when actually it is less than the stated average.
The consequence of type II error is that the ineffective curriculum will not be revised and will be continued in the next year as well. The performance of students might be the same in the coming academic years.
B.
Null hypothesis:
H0: $75
Alternative hypothesis:
H1: > $75
In this context, type I error is the event of concluding that the average sales per customer are higher than $75, when actually it is not higher than $75 per customer.
The consequence of type I error is that $10 coupon will be given out to customers by mistake for two weeks and extra cost will be incurred without a benefit.
In this context, type II error is the event of concluding that the average sales per customer are not higher than $75, when actually it is higher than $75 per customer.
The consequence of type II error is that the $10 coupon will not be given out to deserved customers and they might get dissatisfied and may no longer return to the shop thereby there will be reduction in the revenue in the coming years.
C.
Null hypothesis:
H0: = 10
Alternative hypothesis:
H1: 10
In this context, type I error is the event of concluding that the average dog population is actually some other number, when actually it is 10 a day.
The consequence of type I error is that unwanted investment of a huge amount in research will be done and thereby reduction in the revenue.
In this context, type II error is the event of concluding that the average dog population is 10 a day, when actually it is some other number.
The consequence of type II error is that the store will decide not to invest in research and continue with the current in store average. Thereby the store either may not meet the daily demand or incur extra cost in keeping dogs in store above the daily demand.
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