## Testing a Single Mean

This section shows how to test the null hypothesis that the population mean is equal to some hypothesized value, using a very concrete example. In this example, all the main elements of hypothesis testing come in to play a role.

### Testing a Single Mean

#### Questions

Question 1 out of 9.

You should do the test with $Z$ rather than $t$ when

The numbers are sampled from a normal distribution.

The sample size is large.

The sample standard deviation is known.

The population standard deviation is known.

Question 2 out of 9.

Assume you know the standard deviation of test scores is 10 and that the distribution is normal. You sample 16 scores and find that the sample mean is 25. Find the $p$ value for a two-tailed test of the hypothesis that the population mean is 20.

Question 3 out of 9.

What is the standard deviation of these sample data?

______

Y

-2

1

3

2

-1

0

4

6

Question 4 out of 9.

What is the estimated standard error of the mean based on these sample data? (These are the same data as the previous question).

______

Y

-2

1

3

2

-1

0

4

6

Question 5 out of 9.

What is the value of t testing the null hypothesis that the population mean is 0? (These are the same data as the previous question).

______

Y

-2

1

3

2

-1

0

4

6

Question 6 out of 9.

What is the two-tailed probability value testing the null hypothesis that the population mean is 0? (These are the same data as the previous question).

______

Y

-2

1

3

2

-1

0

4

6

Question 7 out of 9.

Using these data below, what is the t statistic for a single-sample $t$ test (null hypothesis is that $\mu=0)$?

______

Y

0.57

0.92

1.03

0.15

0.96

0.59

1.72

-0.22

Question 8 out of 9.

Using these data below, what is the $t$ statistic for a single-sample $t$ test (null hypothesis is that $\mu=.5$)?

______

Y

1.26

1.52

0.22

0.93

0.34

-0.25

1.22

-0.36

Question 9 out of 9.

Using these data below, what is the two-tailed $p$ value for a single-sample $\mathrm{t}$ test (null hypothesis is that $\mu=.5$)?

______

Y

-0.93

-1.13

1.07

-0.53

1.66

1.70

1.02

0.43