1. For each of the following, state the null and alternative hypotheses, the Typ
ID: 3125862 • Letter: 1
Question
1. 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 descision to implement changes in the current math program at a junior high in Bigcity will be based on a sampleof 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 cirriculum.
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 of 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 reserach to determine the actual average and decide how to accommodate the change.
Explanation / Answer
A.) Null hypothesis : The average score is 89
Alternative Hypothesis : average score less than 89
Probability of type 1 error is decide that the average is less than 89 when it is more than 89.
In such a case, the teachers will change the math program when there is no need for it.
Probability of type 2 error is deciding that the average is 89 when it is actually less than 89.
In this case the students will not get a revised circullum when they actually need it.
B.) Ho : the average sales is $75
H1 : the average sales is more than $ 75
Probability of type 1 error is if the random sample indicates that the average sales is more than $75 when it is actually $75.
In such case the store will give out $10 coupons even when the average is not better.
Probability of type 2 error is that the random sample indicates that the average is $75 when the average is more than $75.
The store will not give out the coupons
C.)
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