Questions and Answers of Essential Statistics

A statistics student has constructed a confidence interval for the mean height of daughters whose mothers are 66 inches tall, and a prediction interval for the height of a particular daughter whose
True or false: When the sample size is large, confidence intervals and hypothesis tests for ????1 are valid even when the assumptions of the linear model are not met.
True or false: If we fail to reject the null hypothesis H0: ????1 = 0, we can conclude that there is no linear relationship between the explanatory variable and the outcome variable.
A confidence interval for a mean response and a prediction interval for an individual response are to be constructed from the same data. True or false: The number of degrees of freedom for the
A confidence interval for ????1 is to be constructed from a sample of 20 points. How many degrees of freedom are there for the critical value?
Explain what the expected frequencies represent in a test of independence.
If the row variable and column variable are interchanged, how are the expected frequencies affected? Is the value of the chi-square statistic affected? Is the number of degrees of freedom affected?
Explain what the expected frequencies represent in a goodness-of-fit test.
Why do large values of ????2 provide evidence against H0? Why don’t small values of ????2 provide evidence against H0?
Can’t read the numbers: Because of printer failure, none of the observed frequencies in the following table were printed, but some of the row and column totals were. Is it possible to construct the
State a conclusion: Can you conclude that the distribution of outcomes differs among the hospitals? Use the ???? = 0.05 level of significance.
Test statistic: Compute the value of the chi-square statistic.
Expected frequencies: Compute the expected frequencies under the null hypothesis of homogeneity.
State a conclusion: Can you conclude that the quality varies among shifts? Use the ???? = 0.01 level of significance.
Test statistic: Compute the value of the chi-square statistic.
Expected frequencies: Compute the expected frequencies under the null hypothesis of homogeneity.
State a conclusion: Can you conclude that education level is independent of gender? Use the ???? = 0.01 level of significance.
Test statistic: Compute the value of the chi-square statistic.
Expected frequencies: Compute the expected frequencies under the null hypothesis of independence.
State a conclusion: Can you conclude that the distribution of boys differs from the binomial with p = 0.5? Use the???? = 0.05 level of significance.
Expected frequencies: Compute the expected frequencies.
Null hypothesis: Let p0 be the probability that a family with four children has no boys, p1 be the probability that a family has one boy, and so on. The null hypothesis is that the number of boys in
Several null hypotheses are tested, and one of them is rejected after the Bonferroni adjustment. Explain why this null hypothesis would also have been rejected if it had been the only one tested.
Meeting specifications: Two extrusion machines that manufacture steel rods are being compared. In a sample of 1000 rods taken from machine A, 960 met specifications regarding length and diameter. In
Spreadsheets: An accounting firm tested two spreadsheet applications to determine whether there is a difference between them in the mean speed with which a standard accounting problem can be solved.
Watching television: The General Social Survey reported that in a sample of 68 men aged 18–25, the mean number of hours of television watched per day was 2.76 with a standard deviation of 2.21. In
Exercise: Medical researchers conducted a study to determine whether treadmill exercise could improve the walking ability of patients suffering from claudication, which is pain caused by insufficient
Sales commissions: A company studied two programs for compensating its sales staff. Nine salespeople participated in the study. In program A, salespeople were paid a higher salary, plus a small
Contaminated water: The concentration of benzene was measured in units of milligrams per liter for a simple random sample of five specimens of untreated wastewater produced at a gas field. The sample
Political polling: In a certain state, a referendum is being held to determine whether the transportation authority should issue additional highway bonds. A sample of 500 voters is taken in county A,
Sick days: A large company is considering a policy of flextime, in which employees can choose their own work schedules within broad limits. The company is interested to determine whether this policy
Five null hypotheses were tested, and the P-values were 0.24, 0.17, 0.03, 0.002, and 0.02. How many of the hypotheses are rejected at the ???? = 0.05 level if the Bonferroni adjustment is made?
Can you reject H0 at the ???? = 0.05 level? State a conclusion.
Refer to Exercise
Compute the value of the test statistic.
Refer to Exercise
A simple random sample of 17 business majors from a certain university had a mean GPA of 2.81 with a standard deviation of 0.27. A simple random sample of 23 psychology majors was selected from the
Can you reject H0 at the ???? = 0.01 level? State a conclusion.
Refer to Exercise
Compute the value of the test statistic.
Refer to Exercise
Two suppliers of machine parts delivered large shipments. A simple random sample of 150 parts was chosen from each shipment.For supplier A, 12 of the 150 parts were defective. For supplier B, 28 of
Can you reject H0 at the ???? = 0.05 level?
Find the value of the test statistic for testing H0: ????d = 15 versus H1: ????d >
In a set of 12 matched pairs, the mean difference was d̄ = 18 and the standard deviation of the differences was sd =
How many degrees of freedom are there for the test statistic? Use the simple method.
For a test of H0: ????1 = ????2 versus H1: ????1 ≠ ????2, the sample sizes were n1 = 15 and n2 =
A sample of size 15 is drawn from a normal population. The sample standard deviation is s1 = 5.2. A sample of size 10 is drawn from another normal population. The sample standard deviation is s2 =
In a test of H0: p1 = p2 versus H1: p1 ≠ p2, the value of the test statistic is z = −1.21. What do you conclude about the difference p1 − p2 at the ???? = 0.05 level of significance?
A simple random sample of 75 people are given a new drug that is designed to relieve pain. After taking this drug for a month, they switch to a standard drug. The question of interest is whether the
A fleet of 100 taxis is divided into two groups of 50 cars each to determine whether premium gasoline reduces maintenance costs. Premium unleaded fuel is used in group A, while regular unleaded fuel
Two machines are used to fill cans. The machines are supposed to fill each can with 12 ounces of liquid. The amounts actually filled follow a normal distribution. A simple random sample of 10 cans is
A simple random sample of 75 people are given a new drug that is designed to relieve pain. A second sample of 50 people are given a standard drug. The question of interest is whether the proportion
Provide an example of two samples that are paired. Explain why these samples are paired.
Provide an example of two samples that are independent. Explain why these samples are independent.
In what ways is the procedure for constructing a confidence interval for the difference between two proportions similar to constructing a confidence interval for one proportion? In what ways is it
Why is it necessary for all values in the confidence interval to be positive to conclude that ????1 > ????2? What would have to be true to conclude that ????1 < ????2?
Interpret computer output: The following output from MINITAB presents a confidence interval for the mean difference between matched pairs.a. Find the point estimate of ????d.b. How many degrees of
Interpret calculator display: The following TI-84 Plus calculator display presents a 95% confidence interval for the mean difference between matched pairs.a. Find the point estimate of ????d.b. How
Interpret computer output: The following MINITAB output presents a confidence interval for the difference between two proportions.a. Find the point estimate of p1 − p2.b. Fill in the blanks: We are
Interpret calculator display: The following TI-84 Plus calculator display presents a 95% confidence interval for the difference between two proportions.a. Find the point estimate of p1 − p2.b. Fill
Interpret computer output: The following MINITAB output display presents a 95% confidence interval for the difference between two means.a. Find the point estimate of ????1 − ????2.b. How many
Interpret calculator display: The following TI-84 Plus calculator display presents a 95% confidence interval for the difference between two means. The sample sizes are n1 = 85 and n2 = 71.a. Find the
Automobile pollution: In a random sample of 340 cars driven at low altitudes, 46 exceeded a threshold for the amount of particulate pollution. In a random sample of 85 cars driven at high altitudes,
Dueling scales: In an experiment to determine whether there is a systematic difference between the weights obtained with two different scales, 10 rock specimens were weighed, in grams, on each scale.
Treating bean plants: In a study to measure the effect of an herbicide on the phosphate content of bean plants, a sample of 75 plants treated with the herbicide had a mean phosphate concentration (in
Polling results: A simple random sample of 400 voters in the town of East Overshoe was polled, and 242 said they planned to vote in favor of a bond issue to raise money for elementary schools. A
Recovery time from surgery: A new postsurgical treatment is being compared with a standard treatment. Seven subjects receive the new treatment, while seven others (the controls) receive the standard
College tuition: Independent random samples of private college and university tuition and fees for the 2012–2013 academic year from California and New York yielded the following data, in
Exercise and heart rate: A simple random sample of seven people embarked on a program of regular aerobic exercise.Their heart rates, in beats per minute, were measured before and after, with the
Don’t construct a confidence interval: An investor is trying to decide in which of two stocks to invest. He examines records for the past 365 days, and finds that the price of stock A increased on
Hatching shrimp eggs: A study of the effect of water pollution on the habitat of shrimp reported that out of 1985 eggs produced by shrimp at the Diesel Creek site in Charleston, South Carolina, 1919
In a poll of 100 voters, 57 said they were planning to vote for the incumbent governor, and 48 said they were planning to vote for the incumbent mayor. Explain why these data should not be used to
Construct a 90% confidence interval for the difference ????1 − ????2.
Refer to Exercise
Compute the margin of error for a 90% confidence interval for the difference????1 − ????2.
Refer to Exercise
Find the critical value for a 90% confidence interval for the difference ????1 − ????2.
Refer to Exercise
A random sample of 76 residents in a small town had a mean annual income of $34,214, with a sample standard deviation of $2171. In a neighboring town, a random sample of 88 residents had a mean
Construct a 99% confidence interval for the difference ????d.
Refer to Exercise
Compute the margin of error for a 99% confidence interval for the difference ????d.
Refer to Exercise
Find the critical value for a 99% confidence interval for ????d.
Refer to Exercise
Eight students in a particular college course are given a pre-test at the beginning of the semester and are then given the same exam at the end to test what they have learned. The exam scores at the
Refer to Exercise 3.Construct a 95% confidence interval for the difference p1 − p2.
Refer to Exercise 3.Compute the margin of error for a 95% confidence interval for the difference p1 − p2.
Find the critical value for a 95% confidence interval for the difference p1 − p2.
Refer to Exercise
In a survey of 300 randomly selected female and 240 male holiday shoppers, 87 of the females and 98 of the males stated that they will wait until the last week before Christmas to finish buying
A sample of 20 weight lifters is tested to see how much weight they can bench press. Ten of them are chosen at random as the treatment group. They participate in a special training program for three
A sample of 15 weight lifters is tested to see how much weight they can bench press. They then follow a special training program for three weeks, after which they are tested again. The samples are
Explain why the power will be greater when the true value of ???? is 20 than when the true value of ???? is 15.
A test will be made of H0: ???? = 12 versus H1: ???? >
In what ways are hypothesis tests for a population mean different from hypothesis tests for a proportion? In what ways are they similar?
Why don’t we need to know the population standard deviation when performing a test about a population proportion?
Why is it important to report the P-value or the test statistic when presenting the results of a hypothesis test?
What does the P-value represent?

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