Notebook + Quiz: Impact of Sample Size

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QUIZ QUESTION: :

Use the first statement in the notebook above to set up the null and alternative hypotheses.

ANSWER CHOICES:

Hypotheses	Statement
The mean height of everyone in the population is equal to 67.60 inches.
The mean height of everyone in the sample is equal to 67.60 inches.
The mean height of everyone in the sample is not equal to 67.60 inches.
The mean height of everyone in the population is equal to 0 inches.
The mean height of everyone in the population is different from 67.60 inches.

SOLUTION:

Hypotheses	Statement
The mean height of everyone in the population is equal to 67.60 inches.
The mean height of everyone in the population is different from 67.60 inches.

QUIZ QUESTION: :

Use the information from question 2 in the notebook to match each description to the correct value.

ANSWER CHOICES:

Description	Value
doesn't look normally distributed
67.88
looks normally distributed
1.4
2.84
3.12
67.60

SOLUTION:

Description	Value
67.88
looks normally distributed
1.4
3.12
67.60

SOLUTION:

Greater than 0.50

Based on the p-value retrieved using the sample of size 5 and any reasonable type I error rate (say 5%),

We have statistically significant evidence to suggest the population mean is not equal to 67.60 inches. (Reject the null)

We do not have statistically significant evidence to suggest the population mean is different from 67.60 inches. (Fail to reject the null)

We do not have enough data to draw any sort of conclusion.

SOLUTION:

We do not have statistically significant evidence to suggest the population mean is different from 67.60 inches. (Fail to reject the null)

QUIZ QUESTION: :

Use your new sampling distribution to match each of the following values to the corresponding statement.

ANSWER CHOICES:

Description	Value
Reject the null - we have evidence the population mean isn't 67.60 inches.
0.0
No change.
No change.
0.18
Fail to reject the null - we do not have evidence the population mean is different from 67.60 inches.
(population standard deviation)/sqrt(5)

SOLUTION:

Description	Value
Reject the null - we have evidence the population mean isn't 67.60 inches.
0.0
No change.
No change.
0.18

In this concept the big takeaway is:

Statistics are confusing.

Even the smallest of differences between a sample mean and a hypothesized population mean are significant when we have large sample sizes.

With large sample sizes, we can do anything we want!

Sampling distributions are the distribution of a sample statistic, and the distribution of a sample mean has a standard deviation of the population divided by the square root of the sample size.

SOLUTION:

Even the smallest of differences between a sample mean and a hypothesized population mean are significant when we have large sample sizes.