Sample Variability and Statistical Inferences

¶ … digit integers {1, 3, 5, 7, 9}.

Sampling distribution of each sample is .04

Mean () Probability P (x)

If a population has a standard deviation ? of 25 units, what is the standard error of the mean if samples of size 16 are selected? Samples of size 36? Samples of size 100?

Standard error for sample size 16 25 / 4= 6.25

Standard error for sample size 36 25/6= 4.17

Standard error for sample size 100 25/10= 2.5

According to Nielsen's Television Audience report, in 2009 the average American home had 2.86 television sets (more than the average number of people per household, at 2.5 people). If the standard deviation for the number of televisions in a U.S. household is 1.2 and a random sample of 80 U.S. households is selected, the mean of this sample belongs to a sampling distribution.

a.What is the shape of this sampling distribution? Normal

b.What is the mean of this sampling distribution?

What is the standard deviation of this sampling distribution? .134

7.18

Consider a normal population with ? = 43 and ? = 5.2. Calculate the z-score for an x of 46.5 from a sample of size 16.

z= 46.5-43 / (5.2 / 4) = 3.5/1.3= 2.69

7.20

What is the probability that the sample of kindergarten children (pages 146-147) has a mean height of less than 39.75 inches?

There are two different sample sizes used in that example- 25 and 100. Using a sample of 100 students, the probability z score is

39.75- 39 / (2/10)= 3.75, and the probability from the table is .999

Unit 6

8.2 A because the results are clustered with low variation.

8.14

A sample of 60 night-school students' ages is obtained in order to estimate the mean age of night-school students. 25.3 years. The population variance is 16.

a.Give a point estimate for ?. 25.3

b.

25.3 ± 1.96(4/?60) and the 95% confidence interval is

24.29 < µ < 25.31

c.Find the 99% confidence interval for ?.

25.3 ± 2.58(4/?60) and the 95% confidence interval is

25.13 < µ < 25.47

8.24 A supplier of highway construction materials claims he can supply an asphalt mixture that will make roads that are paved with his materials less slippery when wet. A general contractor who builds roads wishes to test the supplier's claim. The null hypothesis is "Roads paved with this asphalt mixture are no less slippery than roads paved with other asphalt." The alternative hypothesis is "Roads paved with this asphalt mixture are less slippery than roads paved with other asphalt."

a.Describe the meaning of the two possible types of errors that can occur in the decision when this hypothesis test is completed.

a) A Type I error occurs the null hypothesis is true, but the data suggests that it is false. Using the example provided, a common Type I error would be that the asphalt is no less slippery, but the data suggests it is. A Type II error is failing to reject an incorrect null hypothesis, and a common Type II error in this scenario would be that the asphalt mix is less slippery, but the data suggests it is not.

b) The null hypothesis is a starting point for the decision to be made about the asphalt, because it provides information about whether the particular asphalt mix under consideration is less slippery (and therefore less dangerous) than other products.

A Type II error occurs when the

8.36 Find the test statistic z? and the p-value for each of the following situations.

a.z star= .0555; p value .48