Question

1. a skeptical paranormal researcher claims that the proportion of americans that have seen a ufo is less than 5 in a thousand. identify the type i error for the test.

a) fail to reject the claim that the proportion of americans that have seen a ufo is equal to 5 in a thousand when that proportion is actually less than 5 in a thousand.
b) reject the claim that the proportion of americans that have seen a ufo is equal to 5 in a thousand when that proportion is actually 5 in a thousand.
c) reject the claim that the proportion of americans that have seen a ufo is equal to 5 in a thousand when that proportion is actually less than 5 in a thousand.
d) fail to reject the claim that the proportion of americans that have seen a ufo is equal to 5 in a thousand when that proportion is actually greater than 5 in a thousand.

1. the owner of a football team claims that the mean attendance at games is over 59,100, and he is therefore justified in moving the team to a city with a larger stadium. identify the type ii error for the test.

a) reject the claim that the mean attendance is equal to 59,100 when it is actually 59,100.
b) fail to reject the claim that the mean attendance is equal to 59,100, when it is actually greater than 59,100.
c) fail to reject the claim that the mean attendance is more than 59,100, when it is actually less than 59,100.
d) fail to reject the claim that the mean attendance is equal to 59,100, when it is actually less than 59,100.

1. a cereal company claims that the mean weight of the cereal in its packets is 14 oz. identify the type i error for the test.

a) reject the claim that the mean weight is 14 oz when it is actually 14 oz.
b) reject the claim that the mean weight is 14 oz when it is actually greater than 14 oz.
c) reject the claim that the mean weight is different from 14 oz when it is actually 14 oz.
d) fail to reject the claim that the mean weight is 14 oz when it is actually different from 14 oz.

Explanation:

• Question 18:
• A Type I error is rejecting the null hypothesis when it is actually true.
• The null hypothesis \(H_0:p = 0.005\) (proportion is 5 in a thousand), and the alternative hypothesis \(H_1:p<0.005\).
• Rejecting \(H_0\) (claim that \(p = 0.005\)) when \(H_0\) is true (proportion is actually 5 in a thousand) is a Type I error.
• Question 19:
• A Type II error is failing to reject the null hypothesis when it is false.
• The null hypothesis \(H_0:\mu=59100\), and the alternative hypothesis \(H_1:\mu > 59100\).
• Failing to reject \(H_0\) (claim that \(\mu = 59100\)) when \(H_0\) is false (mean attendance is actually greater than 59100) is a Type II error.
• Question 20:
• A Type I error is rejecting the null hypothesis when it is actually true.
• The null hypothesis \(H_0:\mu = 14\), and the alternative hypothesis \(H_1:\mu

eq14\).

• Rejecting \(H_0\) (claim that \(\mu = 14\)) when \(H_0\) is true (mean weight is actually 14 oz) is a Type I error.

Answer:

• 18) B. Reject the claim that the proportion of Americans that have seen a UFO is equal to 5 in a thousand when that proportion is actually 5 in a thousand.
• 19) B. Fail to reject the claim that the mean attendance is equal to 59,100, when it is actually greater than 59,100.
• 20) A. Reject the claim that the mean weight is 14 oz when it is actually 14 oz.