STS 2610 Test 3

5. b) Give a 95% confidence interval for μ. Assume the gas mileages follow a normal distribution.

stat- t test- confidence interval- 95% =6.07 <u< 6.55

5. a) Give the point estimate for μ, the mean fuel mileage for the fleet using the new fuel catalyst.

stat- t test- confidence interval- 95%- sample mean =6.31

12. g) Give the upper 95% confidence limit for the average percent of males who return over all years when the number of breeding pairs is 34.

Confidence Interval Upper Limit = 65.868

For the United States, the average monthly Internet bill is $39.98 per household. Is the average monthly Internet bill in North Carolina different from the national average? After collecting data, a 90% confidence interval for the average monthly Internet bill in North Carolina is constructed. The resulting interval is (39.79, 43.47). What do you conclude?

Ha=/ 39.98 Ho= 39.98 Fail to reject as we are 90% confident that the actual mean is between those two data points and the average monthly internet bill falls between those data points

9. b) State the hypotheses.

Ho= u <= 6 Ha= u>6

10. a) State the hypotheses.

Ho=u >= 6 Ha= u<6

12. d) Is there evidence that the percent of males who return depends on the number of breeding pairs? Explain.

If the slope is anything besides zero this shows a correlation, so yes they do depend on one another

9. f) Give the p-value of the test.

P Value = 0.008

A 95% confidence interval for a population mean score on a dexterity test is (70, 84). This means a. 95% of all dexterity scores are between 70 and 84. b. I am 95% confident that the sample mean score is between 70 and 84. c. The probability is .95 that the population mean score is between 70 and 84. d. I am 95% confident that the population mean score is between 70 and 84.

d. I am 95% confident that the population mean score is between 70 and 84.

12. c) Give the p-value of the test for H0: β1 = 0 against H1: β1 ≠ 0.

model one p value = 0.0028

10. b) Give the value of the test statistic.

-1.807

10. c) Give the p-value of the test.

0.03

9. h) Which of the following is true? 1. There is sufficient evidence at the 0.05 level of significance that the fuel catalyst increases gas mileage. 2. There is not sufficient evidence at the 0.05 level of significance that the fuel catalyst increases gas mileage.

1. There is sufficient evidence at the 0.05 level of significance that the fuel catalyst increases gas mileage.

9. g) Which of the following is true? 1. We would reject the null hypothesis. 2. We would fail to reject the null hypothesis.

1. We would reject the null hypothesis.

9. i) Which of the following is true? 1. The result is statistically significant at the 0.05 level but not at the 0.10 level. 2. The result is statistically significant at the 0.01 level of significance. 3. The result is not statistically significant at the 0.10 level of significance. 4. The result is statistically significant at the 0.05 level but not at the 0.01 level of significance.

2. The result is statistically significant at the 0.01 level of significance.

10. e) Which of the following is true? 1. There is sufficient evidence at the 0.01 level of significance that the mean approval time for loans at this bank has been reduced. 2. There is not sufficient evidence at the 0.01 level of significance that the mean approval time for loans at this bank has been reduced.

2. There is not sufficient evidence at the 0.01 level of significance that the mean approval time for loans at this bank has been reduced.

10. d) Which of the following is true? 1. We would reject the null hypothesis. 2. We would fail to reject the null hypothesis.

2. We would fail to reject the null hypothesis.

_____% of all 90% confidence intervals contain µ.

90

T Distribution v. Normal Distribution

Both are centered at 0 with their mean and medians at zero and extend in both directions infinitely. The T Distribution is flatter and has fatter tails

What are the degrees of freedom and how does it affect the T curve and the critical values of the T curve

Degrees of Freedom is N-1. As DF increases the T Curve becomes closer to the normal density curve

What is a type II error?

Failing to reject the null when the alternative is true

9. d) What would be the implications of making a Type II error?

Failing to reject the null. This would be stating it improves fuel efficiency and reduces pollutants when it does not

12. i) By hand, calculate the predicted percent of males who return in an individual year when the number of breeding pairs is 36.

Plug into the line equation- 165.35-3.12x = 53.1052

Use the SUV data set from your textbook data sets Chapter 8 to calculate a 90% confidence interval for the mean miles per gallon of 2014 small SUVs. What is the point estimate and 90% error margin?

Point Estimate= estimated mean = 22.85 90% Error Margin = Upper Limit - Point Estimate = 23.48-22.85= 0.63

What is a type I error? What is the probability of a type I error?

Rejecting the null hypothesis when it is true. Alpha is the probability of making this error

9. c) What would be the implications of making a Type I error?

Rejecting the null when it is true. This would be believing that the device does not improve fuel efficiency and reduce pollutants when it does

12. k) When the number of breeding pairs increases by 1, The percent of males who return is expected to decrease by ________.

Slope- 3.12

9. e) Give the value of the test statistic.

T Stat= 2.85

How is the margin of error (and therefore the width of the confidence interval) affected when a) the confidence level is changed?

The higher the confidence level the margin of error increases

How is the margin of error (and therefore the width of the confidence interval) affected when b) the sample size is changed?

The more samples taken the smaller the margin of error becomes

12. j) Give the upper 95% prediction limit for the percent of males who return in an individual year when the number of breeding pairs is 34.

Upper 95% Prediction Interval- =76.09

5. c) What is the error margin for the 95% confidence interval for μ?

Upper Limit - X Bar= 6.55 - 6.31= .24

A quality control inspector must verify whether a machine that packages snack foods is working correctly. The inspector will randomly select a sample of packages and weigh the amount of snack food in each. Assume that the weights of food in packages filled by the machine have a standard deviation of 0.30 ounce. An estimate of the mean amount of snack food in each package must be reported with 99 percent confidence and a margin of error ±0.12 ounce. What would be the minimum sample size for the number of packages the inspector must select?

n= (z*s/e) ^2 99%- z= 2.576 s= .30 e= .12 (2.576*.30/.12)^2= 41.4736 always round up = 42

12. h) Give the predicted percent of males who return in an individual year when the number of breeding pairs is 34.

once again plug in 34 = 59.34

12. f) Give the point estimate for the average percent of males who return over all years when the number of breeding pairs is 34.

plug in 34 = 59.34

12. e) Give the lower 95% confidence limit for β1.

slope lower limit = -4.58

12. b) Find the regression line equation for predicting the percent of males who return from the number of breeding pairs.

stat- regression- simple linear- plug in x and y and submit = 165.35 - 3.12x

12. a) Find the correlation coefficient from the data on merlins (small falcons) in Sweden that were observed for 7 years.

stat- summary stats- correlation = -.925

9. a) Describe the parameter μ that will appear in the hypotheses

u is the average miles per gallon with the device installed