Final Exam Practice

A schoolteacher is worried that the concentration of dangerous, cancer-causing radon gas in her classroom is greater than the safe level of 4pCi/L. The school samples the air for 36 days and finds an average concentration of 4.4pCi/L with a standard deviation of 1pCi/L. The value of the test statistic is ___________.

t35 = 2.40

Which of the following variables is quantitative?

temperature

Suppose the average price for new cars has a mean of $30,100 and a standard deviation of $5,600. Based on this information, what interval of prices would we expect at least 95% of new car prices to fall within?

$18,900 to $41,300

Susan has been on a bowling team for 14 years. After examining all of her scores over that period of time, she finds that they follow a normal distribution. Her average score is 225, with a standard deviation of 13. If during a typical week Susan bowls 16 games, what is the probability that her average score is more than 230?

0.0618

The contingency table below provides frequencies for the preferred type of exercise for people under the age of 35 and those 35 years of age or older. Find the probability that an individual prefers running.

0.3915 = 202/516 = 0.3915

Susan has been on a bowling team for 14 years. After examining all of her scores over that period of time, she finds that they follow a normal distribution. Her average score is 225, with a standard deviation of 13. What is the probability that in a one-game playoff, her score is more than 227?

0.4404 Solution : Given that , mean=μ = 225 standard deviation =σ = 13 P(x > 227) = 1 - P(x < 227) = 1 - P[(x -μ ) / σ< (227 - 225) / 13) = 1 - P(z < 0.15) = 1 - 0.5596 = 0.4404 Probability = 0.4404

According to a study by the Centers for Disease Control and Prevention, about 33% of U.S. births are Caesarean deliveries. Suppose seven expectant mothers are randomly selected. The expected number of mothers who will not have a Caesarean delivery is ______.

4.69 GIVEN: P(C) = 0.33 P(C') = 1 - P(C) = 1 - 0.33 = 0.67 ----------------- Expected number of mothers who will not have a Caesarean delivery = n * P(C') = 7 * 0.67 = 4.69

The salary of teachers in a particular school district is normally distributed with a mean of $50,000 and a standard deviation of $2,500. Due to budget limitations, it has been decided that the teachers who are in the top 2.5% of the salaries would not get a raise. What is the salary level that divides the teachers into one group that gets a raise and one that doesn't?

54,900 =(2,500 *1.96) + 50,000 = 4,900 +50,000 = 54,900

The following histogram represents the number of pages in each book within a collection. What is the frequency of books containing at least 250 but fewer than 300 pages?

7

Professors at a local university earn an average salary of $80,000 with a standard deviation of $6,000. Using Chebyshev's inequality, the percentage of salaries falling between $68,000 and $92,000 is at least __________.

75%

What type of test for population means should be performed when employees are first tested, trained, and then retested?

A t test under dependent sampling.

A 7,000-seat theater is interested in determining whether there is a difference in attendance between shows on Tuesday evening and those on Wednesday evening. Two independent samples of 25 weeks are collected for Tuesday and Wednesday. The mean attendance on Tuesday evening is calculated as 5,500, while the mean attendance on Wednesday evening is calculated as 5,850. The known population standard deviation for attendance on Tuesday evening is 550 and the known population standard deviation for attendance on Wednesday evening is 445. Which of the following is the appropriate decision given a 5% level of significance? The test statistic calculated in Excel with these data is -2.474.

Conclude that the mean attendance differs because the p-value = 0.0136 < 0.05. The p-value=2*P(Z<-2.474) = 2*0.0068 =0.0134

The student senate at a local university is about to hold elections. A representative from the women's sports program and a representative from the men's sports program must both be elected. Two candidates, an incumbent and a challenger, are vying for each position and early polling results are presented next. A hypothesis test must be performed to determine whether the percentages of supporting votes are different between the two incumbent candidates. In a sample of 100 voters, 67 said that they would vote for the women's incumbent candidate. In a separate sample of 100 voters, 55 said they would vote for the men's incumbent candidate. Let p1 and p2 be the proportions of supporting votes for the incumbent candidates representing women's and men's sports programs, respectively. Which of the following is the correct conclusion for the test at αα⁢ = 0.05? Test statistic calculated in Excel is 1.74.

Do not reject H0: p1 = p2 and therefore do not conclude that the proportions differ.

A consumer magazine wants to figure out which of two major airlines lost a higher proportion of luggage on international flights. The magazine surveyed Standard Air (population 1) and Down Under airlines (population 2). Standard Air lost 45 out of 600 bags. Down Under airlines lost 30 of 500 bags. Does Standard Air have a higher population proportion of lost bags on international flights? Which of the following is the appropriate conclusion at the 5% significance level? Test statistic calculated in Excel is .983.

Fail to reject H0; we cannot conclude that the proportion of lost luggage is higher for Standard Air than for Down Under airlines.

You would like to determine if there is a higher incidence of smoking among women than among men in a neighborhood. Let women and men be represented by populations 1 and 2, respectively. Which of the following hypotheses is relevant to this claim?

H0: p1 - p2 ≤ 0, HA: p1 - p2 > 0

A producer of fine chocolates believes that the sales of two varieties of truffles differ significantly during the holiday season. The first variety is milk chocolate while the second is milk chocolate filled with mint. It is reasonable to assume that truffle sales are normally distributed with unknown but equal population variances. Two independent samples of 18 observations each are collected for the holiday period. A sample mean of 12 million milk chocolate truffles sold with a sample standard deviation of 2.5 million. A sample mean of 13.5 million truffles filled with mint sold with a sample standard deviation of 2.3 million. Use milk chocolate as population 1 and mint chocolate as population 2. Which of the following are the appropriate hypotheses to determine if the average sales of the two varieties of truffles differ significantly during the holiday season?

H0: µ1 - µ2 = 0, HA: µ1 - µ2 ≠ 0 population 1= milk chocolate population 2= mint chocolate LET: μ1- be the average sales of population 1 μ2- be the average sales of population 2

Vermont-based Green Mountain Coffee Roasters dominates the market for single-serve coffee in the United States, with its subsidiary Keurig accounting for approximately 70% of sales ("Rivals Try to Loosen Keurig's Grip on Single-Serve Coffee Market," Chicago Tribune, February 26). But Keurig's patent on K-cups, the plastic pods used to brew the coffee, is expected to expire this year, allowing other companies to better compete. Suppose a potential competitor has been conducting blind taste tests on its blend and finds that 47% of consumers strongly prefer its French Roast to that of Green Mountain Coffee Roasters. After tweaking its recipe, the competitor conducts a test with 144 tasters, of which 72 prefer its blend. The competitor claims that its new blend is preferred by more than 47% of consumers to Green Mountain Coffee Roasters' French Roast. Which of the following should be used to develop the null and alternative hypotheses to test this claim?

H0:p ≤ 0.47, HA:p > 0.47

The Institute of Education Sciences measures the high school dropout rate as the percentage of 16-through 24-year-olds who are not enrolled in school and have not earned a high school credential. Last year, the high school dropout rate was 8.1%. A polling company recently took a survey of 1,000 people between the ages of 16 and 24 and found that 6.5% of them are high school dropouts. The polling company would like to determine whether the dropout rate has decreased. When testing whether the dropout rate has decreased, the appropriate hypotheses are _____________.

Ho:p≥0.081,HA:p<0.081

A schoolteacher is worried that the concentration of dangerous, cancer-causing radon gas in her classroom is greater than the safe level of 4pCi/L. The school samples the air for 36 days and finds an average concentration of 4.4pCi/L with a standard deviation of 1pCi/L. To test whether the average level of radon gas is greater than the safe level, the appropriate hypotheses are _____________________.

Ho:μ≤4.0,HA:μ>4.0

A tutor promises to improve GMAT scores of students by more than 50 points after three lessons. To see if this is true, the tutor takes a sample of 49 students' test scores after and before they received tutoring. The mean difference was 53 points better after tutoring, with a standard deviation of the difference equal to 12 points. Let µD denote the mean of the difference: score after tutoring minus score before tutoring. Which of the following is the appropriate conclusion at the 5% significance level? The test statistic calculated in Excel is 1.75.

Reject H0; we can conclude that the mean difference in test scores after and before tutoring is greater than 50 points.

The national average for an eighth-grade reading comprehension test is 73. A school district claims that its eighth-graders outperform the national average. In testing the school district's claim, how does one define the population parameter of interest?

The mean score on the eighth-grade reading comprehension test

A bank is trying to determine which model of safe to install. The bank manager believes that each model is equally resistant to safe crackers but sets up a test to be sure. He hires nine safe experts to break into each of the models, timing each endeavor. The results (in seconds) are given next, paired by expert. Let D be the difference: Time to break Safe 1 minus Time to break Safe 2. The mean of the differences of these nine times is calculated to be 2 seconds. Standard error of the estimate calculated in Excel is 1.3642. Safe 1: 103, 90, 64, 120, 104, 92, 145, 106, 76 Safe 2: 101, 94, 58, 112, 103, 90, 140, 110, 74 Assuming the difference D is normally distributed, which of the following is the 95% confidence interval for μD?

[-1.1458, 5.1458]

A sample of 2,007 American adults was asked how they viewed China, with 17% of respondents calling the country "unfriendly" and 6% of respondents indicating the country was "an enemy". Construct a 95% confidence interval of the proportion of American adults who viewed China as either "unfriendly" or "an enemy."

[0.2116, 0.2484]

A sample of 1,400 American households was asked if they planned to buy a new car next year. Of the respondents, 34% indicated they planned to buy a new car next year. Construct a 98% confidence interval of the proportion of American households who expect to buy a new car next year.

[0.3105, 0.3695]

When comparing two population means, their hypothesized difference _________ .

may assume any value

What is the minimum sample size required to estimate a population mean with 95% confidence when the desired margin of error is E = 1.5? The population standard deviation is known to be 10.75.

n = 198

If the p-value for a hypothesis test is 0.027 and the chosen level of significance is α = 0.05, then the correct conclusion is to ________________.

reject the null hypothesis Because the p-value (0.027) is less than our significance level (0,005)

When testing the difference between two population means under independent sampling, we use the z distribution if _________ .

the population variances are known

A Type I error is committed when we reject the null hypothesis, which is actually true.

true