Question

Reference text for questions 3-4: Suppose a scratch-off lottery game in NC claims that their cards yield an average prize of $1. To test whether the population mean prize (denote \mu ) is different from 0.25, you obtain a random sample of 81 cards. Then, you find that the mean prize in your sample (denote \overline{x} ) is equal to $0.95, and the sample standard deviation (denote s) is equal to $0.12.

3. Assuming the null hypothesis is true, can you estimate the standard error of your sampling distribution without knowing the population standard deviation?

If so, what does this imply regarding your test statistic and critical values?

Select one:

No.

Yes. I can use s to estimate my standard error, and a t-distribution to find my test statistic and critical values.

Yes. I can use s to estimate my standard error, and a z-distribution to find my test statistic and critical values.

Yes. I can use  to estimate my standard error, and a t-distribution to find my test statistic and critical values.

Question 4

What is the value of your test statistic?

Select one:

-3.75

-33.75

2.25

3.75

Not enough information to calculate.

Answer 1

3. Yes. I can use s to estimate my standard error, and a t-distribution to find my test statistic and critical values.

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4. Test statistic:

t = (x̅ - µ)/(s/√n) = (0.95 - 1)/(0.12/√81) = -3.75