10.2 notes

REVIEW:

STATISTICPARAMETER

------

Proportion

------

Mean

------

Std. Deviation

Try this problem…

It has been claimed that the average math SAT score for high school students is 500 points. A random sample of 70 high school students finds that the average math SAT score is 525 points. The standard deviation of this sample is 60 points. Perform a test of significance to see if the average score has gone up. Use a 0.05 level of significance.

1- What are the 3 conditions? Check them:

2- What are the hypotheses?

3-What is the test statistic??

Not _____. Now, we are using ______.

Formula:

4- What is the p-value?

P-Value notes….. Using a t-distribution

This time, the sample size matters even more!

Review: How does sample size affect our normal distribution? Draw the 3 distributions below, each with a center of 50.

SAMPLE SIZE 10

------

50

SAMPLE SIZE 100

------

50

SAMPLE SIZE 1000

------

50

  • Since sample size affects the SPREAD (std. dev.) of the sampling distribution, it affects the p-value.
  • How? Let’s mark the same observation (65) on each of the sampling distributions above.
  • What would the p-value be for the observation of 65 on each of the distributions above?
  • Which of the distributions would have a small p-value (reject Ho)?

So when we are testing a mean, we have to take into account the sample size.

We do this by writing something called:(need to write it down on each problem!)

CALCULATOR:

P-value: tcdf(lower bound, upper bound, df)

Find the p-value for the problem from before:

5- Conclusion:

Still the same….

Conclusion from example above:

Examples:

  1. The EPA wants to show that “the mean carbon monoxide level of air pollution is higher than 4.9.” Does a random sample of readings (with sample results ) present sufficient evidence at the 0.05 level of significance to support the EPA’s claim? Perform a full test of significance.
  1. The estimated U.S. intake of trans-fatty acids is 8 grams per day. Consider a research project involving 150 individuals in which their daily intake of trans-fatty acids was measured. Suppose the average fatty acid intake from this sample was 12.5 grams, with a standard deviation of 7.7 grams. Test to see if the average amount of trans-fatty acids has increased at  = 0.05.
  1. The average stay in days for public hospitals is claimed to be 8.2 days. A sample of 50 such hospitals was selected, and the average stay was found to be 9.1 days with a standard deviation of 1.1 days. Test the hypothesis that the average stay is different from the national average. Use  = 0.01.

Try this problem:

A random sample of size 60 is taken from the weights of babies born at NorthsideHospital during the year 1994. A mean (average) of 6.87 lb and a standard deviation of 1.76 lb were found for the sample. Estimate the true average weight of all babies born in this hospital in 1994, using a 95% confidence interval.

Formula for a confidence interval for a mean (average):

Where do we find the t* from? USE THE CALCULATOR!

Complete the problem from above:

Examples….

  1. A survey was conducted involving 250 families living in a city. The average amount of income tax paid per family in the sample was $3540 with a standard deviation of $1150. Establish and interpret a 99% confidence interval estimate for the taxes paid by families in this city.
  1. Suppose that in a sample of 36 bottles from a certain bottling machine, the machine filled the bottles with an average of 16.1 ounces of cola. The sample had a standard deviation of 0.11 ounces. Give a 90% confidence interval for the mean number of ounces. Interpret this interval.

10.2 WORKSHEET:Complete the following tests and confidence intervals. Be sure to check the conditions for each problem.

  1. We have a random sample of 85 fifth grade students. We find that these 5th graders can do 15 pushups on average, with a standard deviation of 4. According to the President’s Fitness Test data, the national average of pushups for 5th graders is 12. Is there evidence that the average number of pushups has increased? Use a significance level of 0.04.
  1. Using the data from the problem above, create a 98% confidence interval for the true number of pushups for 5th graders. Interpret your interval.
  1. I am doing a test of significance where the significance level (alpha) is 0.05.
  2. If I find a p-value of 0.02, is this significant? Would I reject my Ho?
  1. If I find a p-value of 0.09, is this significant? Would I reject my Ho?
  1. It has been shown that the average height of 18-23 year old females is 63.5.” We take an SRS of 120 18-23 year old females and find that the average height is 66” with a standard deviation of 1.5.” Is there evidence that the true mean height of 18-23 year old females is different than what was claimed? Use a significance level of 0.05.
  1. Using the information in the previous problem, create a 90% confidence interval. Interpret this interval.
  1. I have a confidence interval that is (89.4, 122.5).
  2. What is the sample mean?
  1. What is the margin of error?

10.2 WORKSHEET:Complete the following tests and confidence intervals. Be sure to check the conditions for each problem.

  1. We have a random sample of 85 fifth grade students. We find that these 5th graders can do 15 pushups on average, with a standard deviation of 4. According to the President’s Fitness Test data, the national average of pushups for 5th graders is 12. Is there evidence that the average number of pushups has increased? Use a significance level of 0.04.
  1. Using the data from the problem above, create a 98% confidence interval for the true number of pushups for 5th graders. Interpret your interval.
  1. I am doing a test of significance where the significance level (alpha) is 0.05.
  2. If I find a p-value of 0.02, is this significant? Would I reject my Ho?
  1. If I find a p-value of 0.09, is this significant? Would I reject my Ho?
  1. It has been shown that the average height of 18-23 year old females is 63.5.” We take an SRS of 120 18-23 year old females and find that the average height is 66” with a standard deviation of 1.5.” Is there evidence that the true mean height of 18-23 year old females is different than what was claimed? Use a significance level of 0.05.
  1. Using the information in the previous problem, create a 90% confidence interval. Interpret this interval.
  1. I have a confidence interval that is (89.4, 122.5).
  2. What is the sample mean?
  1. What is the margin of error?