Using Internet Explorer or other web browser you prefer to use, go to the website for your textbook:http://bcs.whfreeman.com/ips8e.Click on "Applets" and then on "Statistical Applets: Confidence Intervals."Read the explanation at the top of the webpage.Use the 95% confidence level until you are told to change.

1.(1 points) What does the m stand for?____________________

2.(1 points)When we calculate a confidence interval in real-life (non-applet) circumstances, do we know what m is?

Circle your answer:Yes No

Press the "SAMPLE" button to create a single confidence interval. Did your confidence interval from your single sample include the true population mean?

Circle your answer:Yes No

3.(2 point)What does the dot in the middle of the confidence interval represent? (Answer with a symbol and in words.)

Try creating some more confidence intervals by hitting the "sample" button several more times.Check to see if all of your confidence intervals include the true population mean.

If you create 100 confidence intervals (click on sample 25 four times), what percentage of your confidence intervals do contain the true population mean (Check the Percent hit value right above the red "RESET" button)?

_____________% of the confidence intervals contain the true population mean.

Now try changing the confidence level and observe the results to your intervals.

4.(1 points)As the confidence level increases, the width of the interval (circle one):

increases / decreases / stays the same

5.(1 points)As the confidence level increases, the percentage of intervals which contain the true population mean (circle one):

increases / decreases / stays the same

Remember, the formula for the confidence interval for the population mean when the population standard deviation is known is:

6.(1 points)As the sample size increases, the width of the interval (circle one):

increases / decreases / stays the same.

7.(1 points)As the confidence level increases, the center of the interval (circle one):

moves right / moves left / stays the same.

Hypothesis Testing

READ THIS:For hypothesis testing, we don't know the true population mean, but we do have a reasonable guess, possibly from previous research, which we call m₀.This number goes in the null hypothesis.The point of hypothesis testing is to see how the true population mean compares to this reasonable guess without having to take a full census.Since we don't know what the population mean really is, we use a simple random sample and calculate a sample statistic.However, we know that every time we take a sample, there is always random variability, so we need to take that into account when we estimate our population parameter.This is why you don't just compare the sample statistic directly to m₀.Instead, we need to see how unusual our sample statistic is if the null hypothesis is true.If the sample statistic isn't too many standard deviations away from m₀, then random chance could explain any discrepancy, and we have no reason to reject the null hypothesis.If the sample statistic is very far away from m₀, then we say that our results are just too weird or extreme to have occurred simply due to random variation alone, and there is something wrong with our null hypothesis.How weird is too weird?We use a cut-off point, called the significance level (a, usually 0.05).If the P-value is less than the significance level, meaning results as extreme as yours have a very small probability of occurring due to random chance, you reject the null hypothesis.

8.(8 points)Fill in the chart below for how we make decisions about conclusions to hypothesis tests.Your answer choices are in boldface type.

P-value > a

P-value a

a)Is the sample mean near or far from the reasonable guess for the population mean m_0?

b)On the Normal curve diagram for this hypothesis test, does the P-value take up a small or big area?

c)Conclusion to the hypothesis test:

Reject H₀,

Do not reject H₀,

Accept H₀

d)There is or is not evidence in favor of the alternative hypothesis.