Never forget that even small effects can be statistically significant if the samples are large. To illustrate this fact, consider a sample of 129 small businesses. During a three-year period, 14 of the 100 headed by men and 5 of the 29 headed by women failed.

(a) Find the proportions of failures for businesses headed by women and businesses headed by men. These sample proportions are quite close to each other. Give the P-value for the test of the hypothesis that the same proportion of women's and men's businesses fail. (Use the two-sided alternative). What can we conclude (Use α=0.05α=0.05)?
The P-value was _______

(b) Now suppose that the same sample proportion came from a sample 30 times as large. That is, 150 out of 870 businesses headed by women and 420 out of 3000 businesses headed by men fail. Verify that the proportions of failures are exactly the same as in part (a). Repeat the test for the new data. What can we conclude?

The P-value was _______

(c) It is wise to use a confidence interval to estimate the size of an effect rather than just giving a P-value. Give 95% confidence intervals for the difference between proportions of men's and women's businesses (men minus women) that fail for the settings of both (a) and (b). (Be sure to check that the conditions are met. If the conditions aren't met for one of the intervals, use the same type of interval for both)

Interval for smaller samples: _____ to _____
Interval for larger samples: _____ to _____

10. One of the major U.S. tire makers wishes to review its warranty for their rainmaker tire. The warranty is for 40,000 miles. The distribution of tire wear is normally distributed with a population standard deviation of 15,000 miles. The tire company believes that the tire actually lasts more than 40,000 miles. A sample of 49 tires revealed that the mean number of miles is 45,000 miles. If we test the hypothesis with a 0.05 significance level, what is the probability of a Type II error if the actual true tire mileage is 45,000 miles? Seleccione una: A. Type II error = 0.4524 B. Type II error = 0.2549 C. Type II error = 0.2451 D. Type II error = 0.4925

Suppose an experiment is conducted where 100 students at BU are measured and their average height is found to be 67.45 inches, and the (sample) standard deviation to be 2.93 inches. Since 100 is a large sample, we use the sample standard deviation as an estimate of the population standard deviation. We may assume that heights are normally distributed.

(a) Suppose that you want to report the 95.45...% confidence interval (i.e., exactly 2 standard deviations). Give the results of this experiment.

(b) Repeat (a) but for the 99.73... % (exactly 3 standard deviations) confidence interval.

(c) Now suppose you want to report the precisely 95.0% confidence interval (which will be slightly less than 2 standard deviations -- find out the exact figure) Repeat (a) using this confidence interval.

(d) Repeat (c) but for the precisely 99.0% confidence interval.

1. The following output was obtained from a regression analysis of the dependent variable Rating and an independent variable Price. (10 points)

1. Use the critical value approach to perform an F test for the significance of the linear relationship between Rating and Price at the 0.05 level of significance.
2. Calculate the coefficient of determination.
3. What percentage of the variability of Rating can be explained by its linear relationship with Price? What is the sample correlation coefficient?
4. What is the estimated regression equation?
5. Use the p-value approach to perform a t test for the significance of the linear relationship between Price and Rating at the 0.05 level of significance.

A researcher surveyed 50 local households and found they had their TV’s on an average of 47.3 hours in a week.   Assume the time Americans have their TV’s turned on is normally distributed with a standard deviation of 6.2 hours.

Construct a 95% confidence interval estimate for the mean time Americans have their TVs turned on in a week.

Show your work for full credit.

random sample of 33 33 professional baseball salaries from 1985 through 2015 was selected. The league of the player​ (American or​ National) was also recorded. Salary​ (in thousands of​ dollars) and league are shown in the accompanying table. Test the hypothesis that there is a difference in the mean salary of players in each league. Assume the distributions are Normal enough to use the​ t-test. Use a significance level of 0.05 0.05.

Let xx be the ages of students in a class. Given the frequency distribution F(x)F(x) above, determine the following probabilities:

(a) P(x=22)=P(x=22)=

(b) P(x≥23 or x<21)=P(x≥23 or x<21)=

(c) P(20≤x<22)=P(20≤x<22)=

1. Calculate the z-scores (to two decimal places) for each observation and write the answers in the last column on the table above.
2. According to Chebyshev’s Theorem, what percentage of the observations should be within 1 standard deviations of the mean? (Hint: be sure to word your answer correctly.) For this question, you do not need to use any data—this is a purely theoretical question asking what Chebyshev predicts for this situation.

Let x be a random variable representing percentage change in neighborhood population in the past few years, and let y be a random variable representing crime rate (crimes per 1000 population). A random sample of six Denver neighborhoods gave the following information. x 26 1 11 17 7 6 y 172 36 132 127 69 53 In this setting we have Σx = 68, Σy = 589, Σx2 = 1172, Σy2 = 72,003, and Σxy = 8920.

(e) For a neighborhood with x = 14% change in population in the past few years, predict the change in the crime rate (per 1000 residents). (Round your answer to one decimal place.) crimes per 1000 residents

(f) Find Se. (Round your answer to three decimal places.)

Se =

(g) Find an 80% confidence interval for the change in crime rate when the percentage change in population is x = 14%. (Round your answers to one decimal place.)

lower limit crimes per 1000 residents

upper limit crimes per 1000 residents

(h) Test the claim that the slope β of the population least-squares line is not zero at the 1% level of significance. (Round your test statistic to three decimal places.)

t =

Find or estimate the P-value of the test statistic.

P-value > 0.250

0.125 < P-value < 0.250

0.100 < P-value < 0.125

0.075 < P-value < 0.100

0.050 < P-value < 0.075

0.025 < P-value < 0.050

0.010 < P-value < 0.025

0.005 < P-value < 0.010

0.0005 < P-value < 0.005

P-value < 0.0005

Conclusion

Reject the null hypothesis, there is sufficient evidence that β differs from 0.

Reject the null hypothesis, there is insufficient evidence that β differs from 0.

Fail to reject the null hypothesis, there is sufficient evidence that β differs from 0.

Fail to reject the null hypothesis, there is insufficient evidence that β differs from 0.

(i) Find an 80% confidence interval for β and interpret its meaning. (Round your answers to three decimal places.)

lower limit

upper limit

Interpretation

For every percentage point increase in population, the crime rate per 1,000 increases by an amount that falls outside the confidence interval.

For every percentage point decrease in population, the crime rate per 1,000 increases by an amount that falls outside the confidence interval.

For every percentage point increase in population, the crime rate per 1,000 increases by an amount that falls within the confidence interval.

For every percentage point decrease in population, the crime rate per 1,000 increases by an amount that falls within the confidence interval.

The Tasty Sub Shop Case: A business entrepreneur uses simple linear regression analysis to predict the yearly revenue for a potential restaurant site on the basis of the number of residents living near the site. The entrepreneur then uses the prediction to assess the profitability of the potential restaurant site. And The QHIC Case: The marketing department at Quality Home Improvement Center (QHIC) uses simple linear regression analysis to predict home upkeep expenditure on the basis of home value. Predictions of home upkeep expenditures are used to help determine which homes should be sent advertising brochures promoting QHIC’s products and services.

Discuss the difference in the type of prediction in both cases and provide rational of the reasons that these predictions were used.

Be sure to respond to the following:

a) What are the dependent and independent values for each case?

b) What are the r values related to the regression. What do these values tell you?

c) Do the independent measures chosen have face validity?

In the case that you would have to use heteroscedastic standard errors but instead falsely use homoscedastic standard errors. What implications would this have regarding unbiasedness, efficiency...

Thanks for your answer

Let Y be a random variable that represents the number of infants in a group of 4,000 who die from asthma in a year. In the United States, the probability that a child dies from an acute asthma attack in a year is 0.0035.

a. What is the mean number of infants who would die in a group of this size?

b. What is the probability that at most four infants out of 4,000 die from asthma in a year?

c. What is the probability that between 6 and 10 infants out of 4,000 die from asthma in a year?

2. What is the consequence of using unconditional logistic regression to analyze the data collected from a 1:M matched case-control study?

Rework problem 28 from section 3.4 of your text, involving the drawing of two balls from a box of colored balls. Assume the box contains 12 balls: 6 red, 3 blue, and 3 yellow. A ball is drawn and its color noted. If the ball is yellow, it is replaced; otherwise, it is not. A second ball is then drawn and its color is noted.

What is the probability that the first ball was yellow, given that the second was red?

The following table consists of one student athlete's time (in minutes) to swim 2000 yards and the student's heart rate (beats per minute) after swimming on a random sample of 10 days. Swim Time Heart Rate 34.13 144 35.74 152 34.73 124 34.03 140 34.14 152 35.73 146 36.16 128 35.56 136 35.39 144 35.58 148 Which point from the data has the largest residual? (x, y) = 35.58,148 Incorrect: Your answer is incorrect. Explain what the residual means in context. Is this point an outlier? An influential point? Explain. (Round your answers to two decimal places.) The residual means that when the swim time is Incorrect: Your answer is incorrect. , the observed heart rate is about Incorrect: Your answer is incorrect. beats less than the predicted rate. When this point is removed, it has a Correct: Your answer is correct. effect on the regression line, so it Correct: Your answer is correct. influential. The point Correct: Your answer is correct. an outlier, because the residual is Correct: Your answer is correct. twice the standard deviation.