# Mathematics

1)

 A politician claims that he is supported by a clear majority of voters. In a recent survey, 35 out of 51 randomly selected voters indicated that they would vote for the politician. Use a 5% significance level for the test. Use Table 1.
a. Select the null and the alternative hypotheses.
 H0: p = 0.50; HA: p ≠ 0.50 H0: p ≤ 0.50; HA: p > 0.50 H0: p ≥ 0.50; HA: p < 0.50
 b. Calculate the sample proportion. (Round your answer to 3 decimal places.)
 Sample proportion
 c. Calculate the value of test statistic. (Round intermediate calculations to 4 decimal places. Round your answer to 2 decimal places.)
 Test statistic
 d. Calculate the p-value of the test statistic. (Round intermediate calculations to 4 decimal places. Round “z” value to 2 decimal places and final answer to 4 decimal places.)
 p-value
e. What is the conclusion?
 Do not reject H0; the politician is not supported by a clear majority Do not reject H0; the politician is supported by a clear majority Reject H0; the politician is not supported by a clear majority Reject H0; the politician is supported by a clear majority

2)

 Consider the following contingency table.
 B Bc A 22 24 Ac 28 26
 a. Convert the contingency table into a joint probability table. (Round your intermediate calculations and final answers to 4 decimal places.)
 B Bc Total A Ac Total
 b. What is the probability that A occurs? (Round your intermediate calculations and final answer to 4 decimal places.)
 Probability
 c. What is the probability that A and B occur? (Round your intermediate calculations and final answer to 4 decimal places.)
 Probability
 d. Given that B has occurred, what is the probability that A occurs? (Round your intermediate calculations and final answer to 4 decimal places.)
 Probability
 e. Given that Ac has occurred, what is the probability that B occurs? (Round your intermediate calculations and final answer to 4 decimal places.)
 Probability
f. Are A and B mutually exclusive events?
 Yes because P(A | B) ≠ P(A). Yes because P(A ∩ B) ≠ 0. No because P(A | B) ≠ P(A). No because P(A ∩ B) ≠ 0.
g. Are A and B independent events?
 Yes because P(A | B) ≠ P(A). Yes because P(A ∩ B) ≠ 0. No because P(A | B) ≠ P(A). No because P(A ∩ B) ≠ 0.

3)

 A hair salon in Cambridge, Massachusetts, reports that on seven randomly selected weekdays, the number of customers who visited the salon were 72, 55, 49, 35, 39, 23, and 77. It can be assumed that weekday customer visits follow a normal distribution. Use Table 2.
 a. Construct a 90% confidence interval for the average number of customers who visit the salon on weekdays. (Round intermediate calculations to 4 decimal places, “sample mean” and “sample standard deviation” to 2 decimal places and “t” value to 3 decimal places, and final answers to 2 decimal places.)
 Confidence interval to
 b. Construct a 99% confidence interval for the average number of customers who visit the salon on weekdays. (Round intermediate calculations to 4 decimal places, “sample mean” and “sample standard deviation” to 2 decimal places and “t” value to 3 decimal places, and final answers to 2 decimal places.)
 Confidence interval to
c. What happens to the width of the interval as the confidence level increases?
 As the confidence level increases, the interval becomes narrower and less precise. As the confidence level increases, the interval becomes wider and less precise.

4)

 Consider the following sample data:
 x 22 36 10 31 11 37 28 32 y 28 44 36 36 34 37 39 33

 b. Calculate b1 and b0. What is the sample regression equation? (Round intermediate calculations to 4 decimal places and final answers to 2 decimal places.)
 y-hat = + x
 c. Find the predicted value for y if x equals 12, 17, and 22. (Round intermediate coefficient values and final answers to 2 decimal places.)
 y-hat If x = 12 If x = 17 If x = 22

5)

 India is the second most populous country in the world, with a population of over 1 billion people. Although the government has offered various incentives for population control, some argue that the birth rate, especially in rural India, is still too high to be sustainable. A demographer assumes the following probability distribution of the household size in India.
 Household Size Probability 1 0.04 2 0.13 3 0.15 4 0.22 5 0.17 6 0.15 7 0.11 8 0.03
 a. What is the probability that there are less than 5 members in a typical household in India? (Round your answer to 2 decimal places.)
 Probability
 b. What is the probability that there are 5 or more members in a typical household in India? (Round your answer to 2 decimal places.)
 Probability
 c. What is the probability that the number of members in a typical household in India is greater than 4 and less than 7 members? (Round your answer to 2 decimal places.)
 Probability

6)

 Consider the following population data:
 22 28 10 12 8
 a. Calculate the range.
 Range
 b. Calculate MAD. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)
 c. Calculate the population variance. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)
 Population variance
 d. Calculate the population standard deviation. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)
 Population standard deviation

7)

 On a particularly busy section of the Garden State Parkway in New Jersey, police use radar guns to detect speeders. Assume the time that elapses between successive speeders is exponentially distributed with a mean of 19 minutes.
 a. Calculate the rate parameter λ. (Round your answer to 4 decimal places.)
 Rate parameter λ
 b. What is the probability of a waiting time less than 13 minutes between successive speeders? (Round your answer to 4 decimal places.)
 Probability
 c. What is the probability of a waiting time in excess of 27 minutes between successive speeders? (Round your answer to 4 decimal places.)
 Probability

8)

 The following ANOVA table was obtained when estimating a multiple regression.
 ANOVA df SS MS F Significance F Regression 2 188,492.30 94,246.15 60.08 4.86E-11 Residual 29 45,490.50 1,568.64 Total 31 233,982.80
 a. Calculate the standard error of the estimate. (Round your answer to 2 decimal places.)
 se
 b-1. Calculate the coefficient of determination. (Round your answer to 4 decimal places.)
 Coefficient of determination
 b-2. Interpret the coefficient of determination.
 The proportion of the variation in x that is explained by the regression model. The proportion of the variation in y that is explained by the regression model.