Question

Reference text for questions 1a-1d:

1a. Suppose a scratch-off lottery game in NC claims that 25% are of their cards yield a prize. To test whether the population proportion of cards containing a prize (denote \pi ) is different from 0.25, you obtain a random sample of 100 cards. Then, you find the proportion of cards containing a prize in your sample (denote (pie the math symbol) ) is equal to 0.21. Which (if any) of the following options correctly specifies the null and alternative hypotheses you are testing? Select one:

a. Null:  = 25%; Alternative:  ≠ 25%

b. Null:  = 0.25 ; Alternative:  ≠ 0.25

c. Null:  = 0.25 ; Alternative:  ≠ 0.25

d. Null:  =   ; Alternative:  ≠

e.None of these options correctly specifies both the null and alternative hypotheses for this test.

1b. If the null hypothesis is true, what is the mean and standard deviation of your sampling distribution?

Select one:

a. Mean = 0.25; Standard Deviation = 0.0433

b. Mean = 0.21; Standard Deviation = 0.0433

c. Mean = 0.21; Standard Deviation = 0.0407

d. Mean = 0; Standard Deviation = 1

e. Mean = 0.25; Standard Deviation = 0.0407

1c. What is the value of your test statistic?

Select one:

a. -0.9237

b. 0.9828

c. -0.9828

d. 0.9237

1d. At a significance level of 0.10, you would...

Select one:

a. Reject the null hypothesis.

b. Fail to reject the null hypothesis.

c. Accept the null hypothesis.

d. Accept the alternative hypothesis.

e. Not reach a conclusion. Not enough information to complete the test.

Answer 1