Ch.9-10 Review
People were polled on how many books they read the previous year. Initial survey results indicate that sequals=14.5 books. Complete parts (a) through (d) below.
((Zα/2•s)/E)²
How many subjects are needed to estimate the mean number of books read the previous year within six books with 90% confidence?
((Zα/2•s)/E)² ((1.645•14.5)/6)=15.8 16
How many subjects are needed to estimate the mean number of books read the previous year within three books with 90% confidence?
((Zα/2•s)/E)² ((1.645•14.5/3)²=63.2 64
How many subjects are needed to estimate the mean number of books read the previous year within six books with 99% confidence?
((Zα/2•s)/E)² ((2.58•14.5)/6)²=38.8 39
Calculate the sample mean for data set II.
98.85
Calculate the sample mean for data set I.
99
Calculate the sample mean for data set III.
99.223
Suppose, in fact, that the proportion of students at the counselor's high school who use electronic cigarettes is 0.224. Was a type I or type II error committed?
A Type II error was committed because the sample evidence led the counselor to conclude the proportion of e-cig users was 0.099, when, in fact, the proportion is higher.
Which intervals, if any, still capture the population mean, 100?
All of the sets
Compare the results to those obtained in part (a). How does decreasing the level of confidence affect the size of the margin of error, E? 105.5 112.5 106.8 111.2
As the percent confidence decreases, the size of the interval decreases.
How does decreasing the sample size affect the margin of error, E? 105.5 112.5 105 113
As the sample size decreases, the margin of error increases.
What impact does the sample size n have on the width of the interval? 82.50 115.5 91.10 106.6 93.49 104.98
As the sample size increases, the width of the interval decreases.
What effect does doubling the required accuracy have on the sample size? 16 64
Doubling the required accuracy nearly quadruples the sample size.
According to the Centers for Disease Control and Prevention, 9.9% of high school students currently use electronic cigarettes. A high school counselor is concerned the use of e-cigs at her school is higher. Complete parts (a) through (c) below. Determine the null and alternative hypotheses. H₀: H₁:
H₀:p=.099 H₁:p>.099
According to a food website, the mean consumption of popcorn annually by Americans is 55 quarts. The marketing division of the food website unleashes an aggressive campaign designed to get Americans to consume even more popcorn. Complete parts (a) through (c) below. Determine the null and alternative hypotheses. H₀: H₁:
H₀:µ=55 H₁:µ>55
Compare this result to part (a). How does increasing the level of confidence in the estimate affect sample size? Why is this reasonable? 16 39
Increasing the level of confidence increases the sample size required. For a fixed margin of error, greater confidence can be achieved with a larger sample size.
Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed?
No, the population needs to be normally distributed.
A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, µ is found to be 109, and the sample standard deviation, s, is found to be 10. Construct a 90% confidence interval about μ if the sample size, n, is 24.
Stats Tests 8 Tinterval 105.5 112.5
A simple random sample of size n equals n=40 is drawn from a population. The sample mean is found to be x̄=120.9 and the sample standard deviation is found to be s=12.6. Construct a 99% confidence interval for the population mean. Lower and Upper Bound
Stats Tests 8 Tinterval 115.51 126.29
Suppose that the data value 106 was accidentally recorded as 061. For each data set, construct a 95% confidence interval using the misentered data. A 95% confidence interval for data set I is:
Stats Tests 8 Tinterval 73.72 113.03
For each data set, construct a 95% confidence interval about the population mean. Data Set I
Stats Tests 8 Tinterval 82.50 115.5
A 95% confidence interval for data set II is:
Stats Tests 8 Tinterval 87.95 105.25
For each data set, construct a 95% confidence interval about the population mean. Data Set II
Stats Tests 8 Tinterval 91.10 106.6
A 95% confidence interval for data set III is:
Stats Tests 8 Tinterval 91.45 104.01
For each data set, construct a 95% confidence interval about the population mean. Data Set III
Stats Tests 8 Tinterval 93.49 104.98
A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, µ is found to be 109, and the sample standard deviation, s, is found to be 10. Construct an 90% confidence interval about muμ if the sample size, n, is 19.
Stats Tests 8 Tinterval 105 113
A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, µ is found to be 109, and the sample standard deviation, s, is found to be 10. Construct an 70% confidence interval about muμ if the sample size, n, is 24.
Stats Tests 8 Tinterval 106.8 111.2
Suppose, in fact, the mean annual consumption of popcorn after the marketing campaign is 55 quarts. Has a Type I or Type II error been made by the marketing department? If we tested this hypothesis at the α=00.01 level of significance, what is the probability of committing this error? Select the correct choice below and fill in the answer box within your choice.
The marketing department committed a Type I error because the marketing department rejected the null hypothesis when it was true. The probability of making a Type I error is 0.01
Which of the following is the concept illustrated with the misentered data?
The procedure for constructing the confidence interval is robust. The larger the sample size, the more resistant the mean. Therefore, the confidence interval is more robust.
If the sample data indicate that the null hypothesis should not be rejected, state the conclusion of the high school counselor.
There is not sufficient evidence to conclude that the proportion of high school students exceeds 0.099 at this counselor's high school.
A sample of 846 Americans provides enough evidence to conclude that marketing campaign was effective. Provide a statement that should be put out by the marketing department.
There is sufficient evidence to conclude that the mean consumption of popcorn has risen.