STP Exam 3 Review

Which of the following is not equivalent to the other​ three?

Dependent variable

Randomly selected deaths from car crashes were​ obtained, and the results are obtained in the accompanying table. Use a 0.05 significance level to test the claim that car crash fatalities occur with equal frequency on the different days of the week. How might the results be​ explained? Why does there appear to be an exceptionally large number of car crash fatalities on​ Saturday? Day # of Fatalities Sun. 144 Mon. 101 Tues. 104 Wed. 93 Thurs. 108 Fri. 136 Sat. 148 What is the conclusion for this hypothesis​ test? How might the results be​ explained? Why does there appear to be an exceptionally large number of car crash fatalities on​ Saturday?

Determine the null and alternative hypotheses. H0​: Fatalities occur with the same frequency on the different days of the week. H1​: At least one day has a different frequency of fatalities than the other days. Calculate the test​ statistic, χ2. ==> χ2=26.026 Calculate the​ P-value. ==> P-value=0.0000.000 Because the​ P-value is less than or equal to the significance​ level, reject H0. There is sufficient evidence to warrant rejection of the claim that car crash fatalities occur with equal frequency on the different days of the week. People are more likely to drive more on the​ weekends, and may be more likely to drink and drive on weekends.

Which of the following is NOT a requirement to conduct a​ goodness-of-fit test?

For each​ category, the observed frequency is at least 5.

Which of the following is NOT a requirement of conducting a hypothesis test for independence between the row variable and column variable in a contingency​ table?

For every cell in the contingency​ table, the observed​ frequency, O, is at least 5.

Adverse reactions of a drug used to help patients continue their abstinence from the use of alcohol have been studied in clinical​ trials, and the accompanying table summarizes results for digestive system effects among patients from different treatment groups. Use a 0.05 significance level to test the claim that experiencing an adverse reaction in the digestive system is independent of the treatment group. Does the drug treatment appear to have an effect on the digestive​ system? Determine the null and alternative hypotheses. Determine the test statistic. Determine the​ P-value of the test statistic. What is the conclusion based on the hypothesis​ test?

H0​: Drug treatment and adverse effects are independent. H1​: Drug treatment and adverse effects are not independent. χ2=39.453 ​P-value=0.000 Since the​ P-value is less than or equal to the significance​ level, reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that experiencing an adverse reaction in the digestive system is independent of the treatment group. The drug treatment appears to decrease adverse effects on the digestive system.

Randomly selected deaths from car crashes were​ obtained, and the results are obtained in the accompanying table. Use a 0.05 significance level to test the claim that car crash fatalities occur with equal frequency on the different days of the week. How might the results be​ explained? Why does there appear to be an exceptionally large number of car crash fatalities on​ Saturday? Day # of Fatalities Sun. 125 Mon. 106 Tues. 99 Wed. 95 Thurs. 96 Fri. 134 Sat. 149 Determine the null and alternative hypotheses. Calculate the test​ statistic, χ2. Calculate the​ P-value. What is the conclusion for this hypothesis​ test? How might the results be​ explained? Why does there appear to be an exceptionally large number of car crash fatalities on​ Saturday?

H0​: Fatalities occur with the same frequency on the different days of the week. H1​: At least one day has a different frequency of fatalities than the other days. χ2=23.637 ​P-value=0.000 Because the​ P-value is less than or equal to the significance​ level, reject H0. There is sufficient evidence to warrant rejection of the claim that car crash fatalities occur with equal frequency on the different days of the week. People are more likely to drive more on the​ weekends, and may be more likely to drink and drive on weekends.

A study of seat belt users and nonusers yielded the randomly selected sample data summarized in the accompanying table. Use a 0.05 significance level to test the claim that the amount of smoking is independent of seat belt use. A plausible theory is that people who smoke are less concerned about their health and safety and are therefore less inclined to wear seat belts. Is this theory supported by the sample​ data? Determine the null and alternative hypotheses. Determine the test statistic. Determine the​ P-value of the test statistic. Use a 0.05 significance level to test the claim that the amount of smoking is independent of seat belt use. A plausible theory is that people who smoke are less concerned about their health and safety and are therefore less inclined to wear seat belts. Is this theory supported by the sample​ data?

H0​: The amount of smoking is independent of seat belt use. H1​: The amount of smoking is not independent of seat belt use. χ2=3.367 ​P-Value=0.338 There is not sufficient evidence to reject the claim that the amount of smoking is independent of seat belt use. The theory is not supported by the sample data.

A high school biology class conducted genetics experiments with randomly selected fruit​ flies, and the results in the following table are based on the results that they obtained. Use a 0.05 significance level to test the claim that the observed frequencies agree with the proportions that were expected according to principles of genetics. Characteristic Freq. Expec. Prop. Red​ Eye/ Normal Wing 81 9/16 Sepia​ Eye/ Normal Wing 28 3/16 Red​ Eye/ Vestigial Wing 25 3/16 Sepia​ Eye/ Vestigial Wing 10 1/16 Determine the null and alternative hypotheses. Calculate the test​ statistic, χ2. Calculate the​ P-value. What is the conclusion for this hypothesis​ test?

H0​: The frequency counts agree with the proportions from genetics. H1​: The frequency counts do not agree with the proportions from genetics. χ2=0.296 ​P-value=0.961 Because the​ P-value is greater than the significance​ level, fail to reject H0. There is not sufficient evidence to warrant rejection of the claim that the observed frequencies agree with the proportions that were expected according to principles of genetics.

A popular theory is that presidential candidates have an advantage if they are taller than their main opponents. Listed are heights​ (in centimeters) of randomly selected presidents along with the heights of their main opponents. Complete parts​ (a) and​ (b) below. Height (cm) of President: 194, 180, 169, 177, 198, 174 Height(cm) of Main Opp: 174, 176, 169, 170, 190, 176 a. Use the sample data with a 0.01 significance level to test the claim that for the population of heights for presidents and their main​ opponents, the differences have a mean greater than 0 cm. What are the null and alternative hypotheses for the hypothesis​ test? Identify the test statistic. Identify the​ P-value. What is the conclusion based on the hypothesis​ test? b. Construct the confidence interval that could be used for the hypothesis test described in part​ (a).

H0​: μ=0cm; H1​: μ>0cm t=1.93 ​P-value=0.055 Since the​ P-value is greater than the significance​ level, fail to reject the null hypothesis. There is not sufficient evidence to support the claim that presidents tend to be taller than their opponents. The confidence interval is −4.6 cm < μd < 16.9 cm.

Captopril is a drug designed to lower systolic blood pressure. The systolic blood pressure reading​ (mmHg) of subjects were measured before and after they took the drug. Results are given in the accompanying table​ (based on data from​ "Essential Hypertension: Effect of an Oral Inhibitor of​ Angiotensin-Converting Enzyme," by MacGregor et​ al., British Medical​ Journal, Vol.​ 2). Assume that the paired sample data is a simple random sample and that the differences have a distribution that is approximately normal. Complete parts​ (a) and​ (b). Before: 170, 174, 209, 179, 210, 185, 155, 169, 198, 182, 193, 200 After: 167, 170, 183, 159, 177, 159, 145, 146, 177, 151, 176, 191 a. Use a 0.01 significance level to test the claim that captopril is effective in lowering systolic blood pressure. What are the null and alternative hypotheses for the hypothesis​ test? Identify the test statistic. Identify t

H0​: μd=0 H1​: μd>0 t=6.37 ​P-value=0.000 Since the​ P-value is less than the significance​ level, reject H0. There is sufficient evidence to support the claim that captopril is effective in lowering systolic blood pressure. b. Construct a confidence interval that could be used to test the claim given in part​ (a). The confidence interval is 10.7mmHg < μd < 26.5 mmHg.

Listed below are annual data for various years. The data are weights​ (metric tons) of imported lemons and car crash fatality rates per​ 100,000 population. Construct a​ scatterplot, find the value of the linear correlation coefficient​ r, and find the​ P-value using α=0.05. Is there sufficient evidence to conclude that there is a linear correlation between lemon imports and crash fatality​ rates? Do the results suggest that imported lemons cause car​ fatalities? Lem Imp CFR 230 15.9 266 15.7 357 15.4 482 15.3 534 14.8 What are the null and alternative​ hypotheses? Construct a scatterplot. Choose the correct graph below. The linear correlation coefficient is _______. The test statistic is t = . The​ P-value is ___. Do the results suggest that imported lemons cause car​ fatalities?

H0​: ρ=0 H1​: ρ≠0 r = −0.949 t = −5.210. The​ P-value is 0.014. Because the​ P-value is less than the significance level 0.05​, there is sufficient evidence to support the claim that there is a linear correlation between lemon imports and crash fatality rates for a significance level of α=0.05. The results do not suggest any​ cause-effect relationship between the two variables.

Media periodically discuss the issue of heights of winning presidential candidates and heights of their main opponents. The accompanying table lists the heights​ (cm) from several recent presidential elections. Construct a​ scatterplot, find the value of the linear correlation coefficient​ r, and find the​ P-value of r. Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Should we expect that there would be a​ correlation? Use a significance level of α=0.05. LOADING... Click the icon to view the heights of the candidates.

H0​: ρ=0 H1​:ρ ≠ 0 The test statistic is t=0.03. The​ P-value is 0.975. Because the​ P-value of the linear correlation coefficient is greater than the significance​ level, there is not sufficient evidence to support the claim that there is a linear correlation between the heights of winning presidential candidates and the heights of their opponents. Should we expect that there would be a​ correlation? B. ​No, because presidential candidates are nominated for reasons other than height.

A bicycle safety organization claims that fatal bicycle accidents are uniformly distributed throughout the week. The table on the right shows the day of the week for which 780 randomly selected fatal bicycle accidents occurred. At α=0.01​, can you reject the claim that the distribution is​ uniform? Complete parts a through d below. Day: Mon., Tues., Wed., Thurs., Fri., Sat., Sun. ​Freq: 113, 105, 111, 123, 106, 113, 109 ​(a) State H0 and Ha and identify the claim. Which hypothesis is the​ claim?

H0​:The distribution of fatal bicycle accidents throughout the week is uniform. Ha​: The distribution of fatal bicycle accidents throughout the week is not uniform. a.) H0

The accompanying table shows results from a study in which some dental patients were treated with amalgam restorations and others were treated with composite restorations that do not contain mercury. Use a 0.05 significance level to test for independence between the type of restoration and the presence of any adverse health conditions. Do amalgam restorations appear to affect health​ conditions? Determine the null and alternative hypotheses. Determine the test statistic. Determine the​ P-value of the test statistic. What is the conclusion based on the hypothesis​ test?

H0​:The presence of any adverse health conditions is independent of the type of restoration. H1​:The presence of any adverse health conditions is not independent of the type of restoration. χ2=0.657; P-value=0.418 Since the​ P-value is greater than the significance​ level, fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that the type of restoration and the presence of any adverse health conditions are independent. The results suggest that amalgam restorations do not appear to affect health conditions.

A randomized controlled trial was designed to compare the effectiveness of splinting versus surgery in the treatment of carpal tunnel syndrome. Results are given in the accompanying table. Using a 0.05 significance​ level, test the claim that success is independent of the type of treatment. What do the results suggest about treating carpal tunnel​ syndrome? Determine the null and alternative hypotheses. Determine the test statistic. Determine the​ P-value of the test statistic. What is the conclusion based on the hypothesis​ test?

H0​:The success of the treatment is independent of the type of treatment​ (splinting or​ surgery). H1​: The success of the treatment is not independent of the type of treatment​ (splinting or​ surgery). χ2=5.964 ; P-value=0.015 Since the​ P-value is less than or equal to the significance​ level, reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that success is independent of the type of treatment. The results suggest that surgery treatment is better.

A popular theory is that presidential candidates have an advantage if they are taller than their main opponents. Listed are heights​ (in centimeters) of randomly selected presidents along with the heights of their main opponents. Complete parts​ (a) and​ (b) below. Height (cm) of President: 176, 185, 171, 189, 190, 179 Height(cm) of Main Opp: 170, 178, 179, 176, 195, 182 a. Use the sample data with a 0.05 significance level to test the claim that for the population of heights for presidents and their main​ opponents, the differences have a mean greater than 0 cm. What are the null and alternative hypotheses for the hypothesis​ test? Identify the test statistic. Identify the​ P-value. What is the conclusion based on the hypothesis​ test? b. What feature of the confidence interval leads to the same conclusion reached in part​ (a)?

H0​:μd=0cm H1​: μd>0cm t=0.50 ​P-value=0.320 Since the​ P-value is greater than the significance​ level, fail to reject the null hypothesis. There is not sufficient evidence to support the claim that presidents tend to be taller than their opponents. b. The confidence interval is −5.1 cm < μd < 8.4 cm. Since the confidence interval contains zero, fail to reject the null hypothesis.

Listed below are the numbers of cricket chirps in 1 minute and the corresponding temperatures in °F. Construct a​ scatterplot, and find the value of the linear correlation coefficient r. Is there sufficient evidence to conclude that there is a linear correlation between the number of chirps in 1 minute and the​ temperature? Use a significance level of α=0.05. Chirps in 1m: 888, 1187, 1095, 860, 1208, 1032, 971, 920 Temp. ​(°​F): 70.3, 92.4, 83.5, 75.9, 89.6, 81.8, 72.8, 79.2 What are the null and alternative​ hypotheses? The linear correlation coefficient r is The test statistic t is The​ P-value is

H0​:ρ=0 H1​:ρ≠0 r = 0.902 t = 5.12 p = 0.002​ Because the​ P-value is less than or equal to the significance level 0.05​, reject the null hypothesis. There is sufficient evidence to support the claim that there is a linear correlation between the number of chirps in 1 minute and the temperature in °F for a significance level of α=0.05.

In a randomized​ double-blind, placebo-controlled trial of​ children, an herb was tested as a treatment for upper respiratory infections in children.​ "Days of​ fever" was one criterion used to measure effects. Among 302 children treated with the​ herb, the mean number of days with fever was 0.93​, with a standard deviation of 1.45 days. Among 397 children given a​ placebo, the mean number of days with fever was 0.77 with a standard deviation of 1.06 days. Use a 0.01 significance level to test the claim that the herb affects the number of days with fever. Based on these​ results, does the herb appear to be​ effective? Assume that the two samples are independent simple random samples selected from normally distributed​ populations, and do not assume that the population standard deviations are equal. Let population 1 be children treated with the herb.

Identify the null and alternative hypotheses. H0​: μ1=μ2 H1​: μ1≠μ2 The test statistic is 1.62 The​ P-value is 0.106 Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that the herb affects the number of days with fever. Based on these​ results, the herb does not appear effective in changing the number of days of fever.

Arm circumferences​ (cm) and heights​ (cm) are measured from randomly selected adult females. The 131 pairs of measurements yield x=32.07 ​cm, y=160.64 ​cm, r=0.027​, ​P-value=0.759​, and y=155+0.1628x. Find the best predicted value of y ​(height) given an adult female with an arm circumference of 35.0 cm. Let the predictor variable x be arm circumference and the response variable y be height. Use a 0.05 significance level.

If the regression equation is a good​ model, substitute the given value of x into the regression equation and calculate y. If the regression equation is not a good​ model, the best predicted value of y is the value of y ​(the mean of the​ y-values) regardless of the value of x. Since the​ P-value, 0.759​, is greater than the significance​ level, 0.05, conclude there is no significant linear correlation between the​ variables, so the regression equation is not a good model. ​Therefore, the best predicted value is the mean​ y-value, y=160.64 cm.

A researcher conducts an experiment in which the height of each student is measured in centimeters and those heights are matched with the same​ students' scores on the first biostatistics test. If it is found that r=​0, does that indicate that there is no association between these two​ variables?

No, because while there is no linear​ correlation, there may be a relationship that is not linear.

Which of the following is NOT true for conducting a hypothesis test for independence between the row variable and column variable in a contingency​ table?

Small values of the χ2 test statistic reflect significant differences between observed and expected frequencies.

Preliminary analyses indicate that you can consider the assumptions for using nonpooled​ t-procedures satisfied. Researchers randomly and independently selected 30 prisoners diagnosed with chronic posttraumatic stress disorder​ (PTSD) and 24 prisoners that were diagnosed with PTSD but had since recovered​ (remitted). Chronic: X1=27.9, S1=4, N1=30 Remitted: X2=20.4, S2=2, N2=24 Obtain a 95​% confidence interval for the​ difference, μ1−μ2​, between the mean ages at arrest for prisoners with chronic PTSD and remitted PTSD.

The 95​% confidence interval is from 5.814 to 9.186

Preliminary analyses indicate that you can consider the assumptions for using non-pooled​ t-procedures satisfied. Researchers obtained the following data on the number of acute postoperative days in the hospital using the dynamic and static systems. Obtain a 95​% confidence interval for the​ difference, μ1−μ2​, b/w the mean #s of acute postoperative days in the hospital w/ the dynamic and static systems.​ (Note: n1=12 x1=7.42​, s1=1.56​, n2=6, x2=10.00​, and s2=3.95​)

The 95​% confidence interval is from −6.712 to 1.552

The relative freq. for the null hypothesis of a​ chi-square goodness-of-fit test & the sample size are given. Decide whether assumptions 1 & 2 for using that test are satisfied. Sample size n=70. The relative frequencies are 0.70 , 0.25​, & 0.05.

The assumptions are not satisfied because more than 20% of the expected frequencies are less than 5.

The relative frequencies for the null hypothesis of a​ chi-square goodness-of-fit test and the sample size are given. Decide whether the two assumptions about expected frequencies for using that test are satisfied. Sample​ size: n=100. Relative​ frequencies: 0.45​, 0.20​, 0.30​, 0.05.

The assumptions are satisfied because the expected frequencies are all 1 or more, and none are less than 5.

Arm circumferences​ (cm) and heights​ (cm) are measured from randomly selected adult females. The 155 pairs of measurements yield x=33.39 ​cm, y=160.15 ​cm, r=0.064​, ​P-value=0.429​, and y=159+0.0307x. Find the best predicted value of y ​(height) given an adult female with an arm circumference of 40.0 cm. Let the predictor variable x be arm circumference and the response variable y be height. Use a 0.05 significance level.

The best predicted value is 160.15cm.

Arm circumferences​ (cm) and heights​ (cm) are measured from randomly selected adult females. The 139 pairs of measurements yield x=31.50 ​cm, y=162.02 ​cm, r=0.054​, ​P-value=0.528​, and y=156+0.1787x. Find the best predicted value of y ​(height) given an adult female with an arm circumference of 38.0 cm. Let the predictor variable x be arm circumference and the response variable y be height. Use a 0.05 significance level.

The best predicted value is 162.02 cm.

Express the confidence interval (0.031,0.097) in the form of p−E<p<p+E. ​(The confidence interval is based on the proportion of green​ eyes.)​

0.031<p<0.097

A random sample of 857 births in New York State included 429 males. Construct a 95​% confidence interval estimate of the proportion of males in all births. It is believed that among all​ births, the proportion of males is 0.513. Do these sample results provide strong evidence against that​ belief? Construct a 95​% confidence interval estimate of the proportion of males in all births. Do these sample results provide strong evidence against that​ belief?

0.467<p<0.533 There is not strong evidence against 0.513 as the value of the proportion of males in all births because 0.513 is contained within the 95% confidence interval.

a. What is a​ residual? b. In what sense is the regression line the straight line that​ "best" fits the points in a​ scatterplot?

A residual is a value of y−y​, which is the difference between an observed value of y and a predicted value of y. The regression line has the property that the sum of squares of the residuals is the lowest possible sum.

Which of the following is NOT 1 of the 3 common errors involving​ correlation?

Correlation does not imply causality.

Which of the following is NOT a requirement of testing a claim about the mean of the differences from dependent​ samples?

The degrees of freedom are n−2.

What is meant by saying that a variable has a​ chi-square distribution?

The distribution of the variable has the shape of a special type of​ right-skewed curve.

Which of the following is NOT a property of the linear correlation coefficient​ r?

The linear correlation coefficient r is robust. That​ is, a single outlier will not affect the value of r.

Which of the following is NOT a property of the​ chi-square distribution?

The mean of the​ chi-square distribution is 0.

Are the observed frequencies​ variables? What about the expected​ frequencies? Explain your answers. Are the expected frequencies​ variables? Explain your answer. Choose the correct answer below.

The observed frequencies are​ variables, as they vary from sample to sample. The expected frequencies are not​ variables, as they are determined by the sample size and the distribution in the null hypothesis.

A data set included the daily number of words spoken by 70 randomly selected women and 70 randomly selected men.

The samples are independent because there is not a natural pairing between the two samples.

A data set includes the age at marriage for 240 randomly selected married men and 240 randomly selected married women.

The samples are independent because there is not a natural pairing between the two samples.

Which of the following is NOT a requirement of testing a claim about two population means when σ Subscript 1 and σ Subscript 2 are unknown and not assumed to be​ equal?

The two samples are dependent.

Which of the following is NOT a requirement of testing a claim about two population means when σ1 & σ2 are unknown & not assumed to be​ equal?

The two samples are dependent.

Here is a result stated in a format commonly used in the​ media: "In a survey of 8837 middle school​ students, 10.5% reported using​ e-cigarettes. The margin of error is ±1 percentage​ point." What values do p​, q​, ​n, E, and p​ represent? If the confidence level is 95​%, what is the value of α​?

The value of *p is the sample proportion. The value of *q is found from evaluating 1−p. The value of n is the sample size. The value of E is the margin of error. The value of p is the population proportion. α=0.05

What is the relationship between the linear correlation coefficient r and the slope b1 of a regression​ line?

The value of r will always have the same sign as the value of b1.

For a χ2​-curve with 22 degrees of​ freedom, find χ20.975.

The χ2​-value is 10.982.

Consider a χ2​-curve w/ df=20. Obtain the χ2​-value that has area 0.10 to its left.

The χ2​-value is 12.443.

Researchers conducted a study to determine whether magnets are effective in treating back pain. Pain was measured using the visual analog​ scale, and the results shown below are among the results obtained in the study. Higher scores correspond to greater pain levels. Assume that the two samples are independent simple random samples selected from normally distributed​ populations, and do not assume that the population standard deviations are equal. Complete parts​ (a) to​ (c) below. Reduction in Pain Level After Magnet Treatment ​(μ1​): n=15​, x=0.48​, s=0.86 Reduction in Pain Level After Sham Treatment ​(μ2​): n=15​, x=0.44​, s=1.45

Use a 0.05 sign level. What are the null and alternative​ hypotheses? H0​:μ1=μ2; H1​:μ1>μ2 The test​ statistic is 0.09 &​ P-value is 0.464 Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment. b. −0.71<μ1−μ2<0.79 c. Does it appear that magnets are effective in treating back​ pain? Is it valid to argue that magnets might appear to be effective if the sample sizes are​ larger? It appears that magnets are not effective in treating back​ pain, because 0 is in the confidence interval. Is it valid to argue that magnets might appear to be effective if the sample sizes are​ larger? ​Yes, because increasing the sample size will decrease the​ P-value.

When making predictions based on regression​ lines, which of the following is not listed as a​ consideration?

Use the regression line for predictions only if the data go far beyond the scope of the available sample data.

Which of the following statements about correlation is​ true?

We say that there is a positive correlation between x and y if the​ x-values increase as the corresponding​ y-values increase.

Listed below are the numbers of cricket chirps in 1 minute and the corresponding temperatures in °F. Find the regression​ equation, letting chirps in 1 minute be the independent​ (x) variable. Find the best predicted temperature at a time when a cricket chirps 3000 times in 1​ minute, using the regression equation. What is wrong with this predicted​ temperature? Chirps in 1 min 1049 750 790 1163 927 1102 1183 1160 Temperature ​(°​F) 87 67.4 68.8 89.1 76.1 87 86.3 87.1 Part 1 The regression equation is y=30.130.1+0.05030.0503x. ​(Round the​ y-intercept to one decimal place as needed. Round the slope to four decimal places as​ needed.) Part 2 The best predicted temperature at a time when a cricket chirps 3000 times in 1​ minute, based on the regression​ equation, is 181181°F. ​(Round to the nearest integer as​ needed.) Part 3 What is wrong with this predicted​ temperature?

What is wrong with this predicted​ temperature? A. It is unrealistically high. The value 3000 is far outside of the range of observed values.

A drug is used to help prevent blood clots in certain patients. In clinical​ trials, among 4562 patients treated with the​ drug, 199 developed the adverse reaction of nausea. Construct a 95​% confidence interval for the proportion of adverse reactions. ​a) Find the best point estimate of the population proportion p. ​b) Identify the value of the margin of error E. ​c) Construct the confidence interval. ​d) Write a statement that correctly interprets the confidence interval. Choose the correct answer below.

a) 0.044 ​b) E=0.006 ​c) 0.037<p<0.049 ​d) One has 95​% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.

In a clinical trial of a certain​ drug, 22 subjects experience headaches among the 231 subjects treated with the drug. Construct a 95​% ​(Wald) confidence interval estimate for the proportion of treated subjects who experience​ headaches, completing parts​ (a) through​ (d) below. a. Find the best point estimate of the population proportion. b. Identify the value of the margin of error E. c. Construct the confidence interval. d. Write a statement that correctly interprets the confidence interval. Select the correct choice below and fill in the answer box to complete your choice.

a. 0.095 b. 0.038 c. 0.057 < p < 0.133 d. We have 95​% confidence that the true value of the population proportion of subjects treated with the drug who experience headaches actually is between the confidence​ interval's lower and upper limits.

In a clinical trial of a certain​ drug, 22 subjects experience headaches among the 222 subjects treated with the drug. Construct a 90​% ​(Wald) confidence interval estimate for the proportion of treated subjects who experience​ headaches, completing parts​ (a) through​ (d) below. a. Find the best point estimate of the population proportion. b. Identify the value of the margin of error E. c. Construct the confidence interval. d. Write a statement that correctly interprets the confidence interval.

a. 0.099 b. 0.033 c. 0.066<p<0.132 d. We have 90​% confidence that the true value of the population proportion of subjects treated with the drug who experience headaches actually is between the confidence​ interval's lower and upper limits.

You want to estimate the percentage of adults who believe that passwords should be replaced with biometric security​ (such as​ fingerprints). How many randomly selected adults must you​ survey? Assume that you want to be 95​% confident that the sample percentage is within 2.1 percentage points of the true population percentage. Complete parts​ (a) through​ (c) below. a. Assume that nothing is known about the percentage of adults who believe that passwords should be replaced with biometric security. b. Assume that a prior survey suggests that about 45​% of adults believe that biometric security should replace passwords. c. Does the additional survey information from part​ (b) have much of an effect on the sample size that is​ required?

a. The sample size needed is 2178. b. The sample size needed is 2156. c. The additional survey information from part​ (b) causes the required sample size to change by less than ​10%. Based on​ this, the additional survey information causes no significant change in the sample size that is required.

You want to estimate the percentage of adults who believe that passwords should be replaced with biometric security​ (such as​ fingerprints). How many randomly selected adults must you​ survey? Assume that you want to be 99​% confident that the sample percentage is within 2.6 percentage points of the true population percentage. Complete parts​ (a) through​ (c) below. a. Assume that nothing is known about the percentage of adults who believe that passwords should be replaced with biometric security. b. Assume that a prior survey suggests that about 47​% of adults believe that biometric security should replace passwords. c. Does the additional survey information from part​ (b) have much of an effect on the sample size that is​ required?

a. The sample size needed is 2459. b. The sample size needed is 2445. c. The additional survey information from part​ (b) causes the required sample size to change by less than ​10%. Based on​ this, the additional survey information causes no significant change in the sample size that is required.

A study of 420,078 cell phone users found that 0.0317​% of them developed cancer of the brain or nervous system. Prior to this study of cell phone​ use, the rate of such cancer was found to be 0.0324​% for those not using cell phones. Complete parts​ (a) and​ (b). a. Use the sample data to construct a 90​% confidence interval estimate of the percentage of cell phone users who develop cancer of the brain or nervous system. b. Do cell phone users appear to have a rate of cancer of the brain or nervous system that is different from the rate of such cancer among those not using cell​ phones? Why or why​ not?

a.) 0.027%<p<0.036​% b.) No​, because 0.0324​% is included in the confidence interval.

a. Using the pairs of values for all 10 ​points, find the equation of the regression line. b. After removing the point with coordinates (2,3)​, use the pairs of values for the remaining 9 points and find the equation of the regression line. c. Compare the results from parts​ (a) and​ (b). Ten points are plotted with nine points, (4, 6), (5, 6), (6, 6), (4, 7), (5, 7), (5, 7), (6, 7), (4, 8), (5, 8), and (6, 8), forming a square and the tenth point (2, 3) being below and to the left of the square. a. What is the equation of the regression line for all 10 ​points? Part 2 b. What is the equation of the regression line for the set of 9 ​points? c. Choose the correct description of the results below.

a.) y=33+0.766x b.) y= 77 c.) The removal of the point has a significant impact on the regression line.

A study of 420,000 cell phone users found that 0.0319​% of them developed cancer of the brain or nervous system. Prior to this study of cell phone​ use, the rate of such cancer was found to be 0.0336​% for those not using cell phones. Complete parts​ (a) and​ (b). a. Use the sample data to construct a 95​% confidence interval estimate of the percentage of cell phone users who develop cancer of the brain or nervous system. b. Do cell phone users appear to have a rate of cancer of the brain or nervous system that is different from the rate of such cancer among those not using cell​ phones? Why or why​ not?

a.)0.027​% < p < 0.037​% b.) No​, because 0.0336​% is included in the confidence interval. Your answer is correct.

A​ ____________ is a table in which frequencies correspond to two variables.

contingency table

A​ __________ exists between two variables when the values of one variable are somehow associated with the values of the other variable.

correlation

Listed below are body temperatures from five different subjects measured at 8 AM and again at 12 AM. Find the values of d and sd. In​ general, what does μd ​represent? Temp (°F) at 8 AM Temp (°F) at 12 AM 98.2 98.8 98.6 98.9 97.2 97.4 97.7 97.3 97.3 97.7 Let the temperature at 8 AM be the first​ sample, and the temperature at 12 AM be the second sample. Find the values of d and sd. In​ general, what does μd ​represent?

d=−0.22 sd= 0.38 The mean of the differences from the population of matched data

Listed below are body temperatures from five different subjects measured at 8 AM and again at 12 AM. Find the values of d and sd. In​ general, what does μd ​represent? Temperature (°F) at 8 AM: 98.3, 99.1, 97.5, 97.7, 97.4 Temperature (°F) at 12 AM:98.8, 99.7, 97.7, 97.6, 97.8 Let the temperature at 8 AM be the first​ sample, and the temperature at 12 AM be the second sample. Find the values of d and sd. In​ general, what does μd ​represent?

d=−0.32 sd=0.28 The mean of the differences from the population of matched data

Two samples are​ ________________ if the sample values are paired.

dependent

A​ _____________ is used to test the hypothesis that an observed frequency distribution fits​ (or conforms​ to) some claimed distribution.

goodness-of-fit test

Two samples are​ ____________ if the sample values from one population are not related to or somehow naturally paired or matched with the sample values from the other population.

independent

Paired sample data may include one or more​ ___________, which are points that strongly affect the graph of the regression line.

influential points

A straight line satisfies the​ __________________ if the sum of the squares of the residuals is the smallest sum possible.

least-squares property

The​ ______________ measures the strength of the linear correlation between the paired quantitative​ x- and​ y-values in a sample.

linear correlation coefficient r

In a​ scatterplot, a(n)​ ______________ is a point lying far away from the other data points.

outlier

Express the confidence interval 0.222<p<0.444 in the form of p±E. ​(The confidence interval is based on the proportion of brown​ eyes.)

p±E=0.333 ± 0.111

Police sometimes measure shoe prints at crime scenes so that they can learn something about criminals. Listed below are shoe print​ lengths, foot​ lengths, and heights of males. Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Based on these​ results, does it appear that police can use a shoe print length to estimate the height of a​ male? Use a sign. level of α=0.01. Shoe Print​ (cm): 30.4, 30.4, 31.5, 31.7, 27.5 Foot Length​ (cm): 25.0, 26.1, 27.3, 27.2, 25.2 Height​ (cm): 173.7, 172.4, 185.2, 170.4, 169.4 The linear correlation coefficient is Determine the null and alternative hypotheses. The test statistic is The​ P-value is Based on these​ results, does it appear that police can use a shoe print length to estimate the height of a​ male?

r=0.494. H0​:=0 H1​:≠0 t=0.98. p=0.398. Because the​ P-value of the linear correlation coefficient is greater than the significance​ level, there is not sufficient evidence to support the claim that there is a linear correlation between shoe print lengths and heights of males. No​, because shoe print length and height do not appear to be correlated.

Use the given data set to complete parts​ (a) through​ (c) below.​ (Use α=​0.05.) x: 10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5 y: 9.15, 8.14, 8.73, 8.76, 9.25, 8.11, 6.13, 3.09, 9.13, 7.27, 4.74 b. Find the linear correlation​ coefficient, r, then determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables. The linear correlation coefficient is Using the linear correlation coefficient found in the previous​ step, determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables. Choose the correct answer below. c. Identify the feature of the data that would be missed if part​ (b) was completed without constructing the scatterplot. Choose the correct answer below.

r=0.816. There is sufficient evidence to support the claim of a linear correlation between the two variables. The scatterplot reveals a distinct pattern that is not a​ straight-line pattern.

Given a collection of paired sample​ data, the​ ____________________ y=b Subscript 0 + b Subscript 1x algebraically describes the relationship between the two​ variables, x and y.

regression equation

For a pair of sample​ x- and​ y-values, the​ ______________ is the difference between the observed sample value of y and the​ y-value that is predicted by using the regression equation.

residual

When determining whether there is a correlation between two​ variables, one should use a​ ____________ to explore the data visually.

scatter-plot

Use the given data to find the equation of the regression line. Examine the scatterplot and identify a characteristic of the data that is ignored by the regression line. x y 14 20.11 10 18.25 11 19.14 13 20.06 9 17.10 4 7.11 8 15.65 5 9.66 12 19.74 7 13.94 6 11.94 Identify a characteristic of the data that is ignored by the regression line.

y=4.00+1.30x The data has a pattern that is not a straight line. Your answer is correct.

Listed below are the overhead widths​ (cm) of seals measured from photographs and weights​ (kg) of the seals. Find the regression​ equation, letting the overhead width be the predictor​ (x) variable. Find the best predicted weight of a seal if the overhead width measured from a photograph is 1.9 ​cm, using the regression equation. Can the prediction be​ correct? If​ not, what is​ wrong? Use a significance level of 0.05. Overhead Width​ (cm): 7.2, 7.4, 9.7, 9.4, 8.7, 8.3 Weight​ (kg): 144, 183, 279, 239, 231, 219 The regression equation is y= The best predicted weight for an overhead width of 1.9 ​cm, based on the regression​ equation, is Can the prediction be​ correct? If​ not, what is​ wrong?

y=−154+43.8x. regression​ equation, is −70.8 kg. The prediction cannot be correct because a negative weight does not make sense. The width in this case is beyond the scope of the available sample data.

The data show systolic and diastolic blood pressure of certain people. Find the regression​ equation, letting the systolic reading be the independent​ (x) variable. If one of these people has a systolic blood pressure of 150 mm​ Hg, what is the best predicted diastolic blood​ pressure? Systolic: 139, 118, 145, 133, 141, 138, 139, 136 Diastolic:101, 61, 82, 74, 104, 79, 74, 74 What is the regression​ equation? What is the best predicted diastolic blood​ pressure?

y=−78.33+1.17x y=81.1

Find the critical value zα/2 that corresponds to the confidence level 91.5​%.

zα/2 = 1.72

Find the critical value zα/2 that corresponds to the confidence level 81.5​%.

zα/2=1.33

Find the critical value zα/2 that corresponds to the confidence level 89​%.

zα/2=1.60

Which of the following is NOT true of the​ goodness-of-fit test?

​Goodness-of-fit hypothesis tests may be​ left-tailed, right-tailed, or​ two-tailed.