Stats Test #3 Study Guide
Complete the statement by filling in the blanks. A research hypothesis is always expressed in terms of ________ __________ because we are interested in making statements about the _________ based on _______ statistics. A) sample; statistics; population; sample B) population; parameters; population; sample C) population; parameters; sample; population D) population; statistics; population; parameter
B) population; parameters; population; sample
A researcher conducts a hypothesis test on a population proportion. Her null and alternative hypothesis are H0: p = 0.6 and Ha: p < 0.6. The test statistic and p-value for the test are z = -1.51 and p-value = 0.0655. For a significance level of ΅ = 0.05, choose the correct conclusion regarding the null hypothesis. A) There is sufficient evidence to accept the null hypothesis that the population proportion is equal to 0.6. B) None of these. C)There is sufficient evidence to conclude that the population proportion is significantly different from 0.6. D)There is insufficient evidence to reject the null hypothesis that the population proportion is equal to 0.6.
D)There is insufficient evidence to reject the null hypothesis that the population proportion is equal to 0.6.
(Solve Problem) Read the following problem description then choose the correct null and alternative hypothesis. A new drug is being tested to see whether it can reduce the rate of food-related allergic reactions in children aged 1 to 3 with food allergies. The rate of allergic reactions in the population of concern is 0.03. A) H0: p = 0.03; Ha: p > 0.03 B) H0: p < 0.03; Ha: p = 0.03 C) H0: p = 0.03; Ha: p < 0.03 D) H0: p 0.03; Ha: p = 0.03
C) H0: p = 0.03; Ha: p < 0.03
From the TI-84 graphing calculator screenshots below, choose the screenshot whose shaded area correctly depicts the following hypothesis test results: H0: p = 0.15, Ha: p J 0.15, ΅ = 0.05, z = -1.82, p-value = 0.0688 *graphs* A) A:.931241 LOW: -1.82 iup:1.82 B) A: .034379 (shaded more on left) LOW: -10 lup: -1.82 C) A: .034379 LOW: -10 lup: -1.82 (Shaded on both let and right side)
*graphs* C) A: .034379 LOW: -10 lup: -1.82 (Shaded on both let and right side)
Use the following information to answer the question. A janitor at a large office building believes that his supply of light bulbs has a defect rate that is different than the defect rate stated by the manufacturer. The janitor's null hypothesis is that the supply of light bulbs has a defect rate of p = 0.09 (the light bulb manufacturer's stated defect rate). Suppose we do a hypothesis test with a significance level of 0.01. Symbolically, the null and alternative hypothesis are as follows: H0: p = 0.09 and Ha: p > 0.09. *Suppose the janitor tests 300 light bulbs and finds that 33 bulbs are defective. What value of the test 5) statistic should he report? Round to the nearest hundredth. A) z = -1.21 B) z = 2.17 C) z = -2.17 D) z = 1.21
D) z = 1.21
A researcher believes that the proportion of women who exercise with a friend is greater than the proportion of men. He takes a random sample from each population and records the response to the question, "Have you exercised with a friend at least once in the last seven days?" The null hypothesis is H0: pwomen = pmen. Choose the correct alternative hypothesis A) Ha: pwomen > pmen B) Ha: pwomen < pmen C) Ha: p = 0 D) Ha: pwomen =/ pmen
A) Ha: pwomen > pmen
Suppose a city official conducts a hypothesis test to test the claim that the majority of voters support a proposed tax to build sidewalks. Assume that all the conditions for proceeding with a one-sample test on proportions have been met. The calculated test statistic is approximately 1.40 with an associated p-value of approximately 0.081. Choose the conclusion that provides the best interpretation for the p-value at a significance level of = 0.05. A) If the null hypothesis is true, then the probability of getting a test statistic that is as extreme or more extreme than the calculated test statistic of 1.40 is 0.081. This result is not surprising and could easily happen by chance. B) The p-value should be considered extreme; therefore the hypothesis test proves that the null hypothesis is true. C) If the null hypothesis is true, then the probability of getting a test statistic that is as extreme or more extreme than the calculated test statistic of 1.40 is 0.081. This result is surprising and could not easily happen by chance. D) None of these.
A) If the null hypothesis is true, then the probability of getting a test statistic that is as extreme or more extreme than the calculated test statistic of 1.40 is 0.081. This result is not surprising and could easily happen by chance.
(Solve the problem) Read the following problem description then choose the correct null and alternative hypothesis. A 1) new drug is being tested to see whether it can reduce the rate of asthma attacks in children ages 5 to 14. The rate of asthma attacks in the population of concern is 0.0744. A) H0: p > 0.0744; Ha: p 0.0744 B) H0: p = 0.0744; Ha: p < 0.0744 C) H0: p = 0.0744; Ha: p > 0.0744 D) H0: p < 0.0744; Ha: p < 0.0744
B) H0: p = 0.0744; Ha: p < 0.0744
Suppose that the following is to be tested: H0: p = 0.35 and Ha: p > 0.35. Calculate the observed z-statistic for the following sample data: Forty out of eighty test subjects have the characteristic of interest. Round to the nearest hundredth. A) z = -1.87 B) z = -0.94 C) z = 2.81 D) z = 1.88
C) z = 2.81
Which of the following is not a condition that must be checked before proceeding with a two-sample test? A) Each sample must be a random sample. B) The samples must be independent of each other. C) Both samples must be large enough so that the product of each sample size (n1 and n2) and the pooled estimate, p, is greater than or equal to 10. D) All of these are conditions that must be checked to proceed with a two-sample test
D) All of these are conditions that must be checked to proceed with a two-sample test
Suppose you are testing your friend to see whether she can tell the difference between the name brand and generic peanut butter. You give her 70 samples selected randomly, half from the name brand and half from the generic brand. The null hypothese is that she is just guessing and should get about half right. Explain what the first kind of error would be in this case (when you reject the null hypothesis when it is actually true) A) The first kind of error would be saying that your friend cannot tell the difference between the two kinds of peanut butter, when she really cannot. B)The first kind of error would be saying that your friend can tell the difference between the two kinds of peanut butter, when she really cannot. C)The first kind of error would be saying that your friend can tell the difference between the two kinds of peanut butter, when she really can. D)The first kind of error would be saying that your friend can not tell the difference between the two kinds of peanut butter, when she really can
B)The first kind of error would be saying that your friend can tell the difference between the two kinds of peanut butter, when she really cannot.
A researcher is wondering whether the drinking habits of adults in a certain region of the country are in the same proportion as the general population of adults. Suppose a recent study stated that the proportion of adults in the general population who reported drinking once a week or less in the last month was 0.26. The null hypothesis for this test is H0: p = 0.26 and the alternative hypothesis is Ha: p < 0.26. The researcher collected data from 150 surveys he handed out at a busy park located in the region. ^ *To continue the study into the drinking habits of adults, the researcher decides to collect data from adults working in "white collar" jobs to see whether their drinking habits are in the same proportion as the general public. The null hypothesis for this test is H0: p = 0.26 and the alternative hypothesis is Ha : p < 0.26 . The researcher collected data from a random sample of 120 adults with "white collar" jobs of which 25 stated that they drank once a week or less in the last month. Assume that the conditions that must be met in order for us to use the N (0,1) distribution as the sampling distribution are satisfied. Find the values of the sample proportion, p, and the test statistic. Round all values to the nearest thousandth. A) ^ p = 0.75, z =-1.32 B) ^p = 0.30, z = 0.803 C) ^p = 0.208, z =-0.250 D) ^p = 0.208, z =-1.290
D) ^p = 0.208, z =-1.290
Which statement best describes the significance level of a hypothesis test? A) The probability of rejecting the null hypothesis when the null hypothesis is true. B) The probability of failing to reject the null hypothesis when the null hypothesis is not true. C) The probability of rejecting the null hypothesis when the null hypothesis is not true. D) None of these
A) The probability of rejecting the null hypothesis when the null hypothesis is true.
(Solve the problem) Two researchers are comparing a blood pressure reducing drug with a two-sided alternative hypothesis. Their test statistics show that the following z values: z1 = 1.87 and z2 =ȱƺ2.45. Which one of these have the smaller p-value and why? A) z1 = 1.87 value because it is closer to the mean. B)z2 =-2.45 because the z-value indicates almost two and a half standard deviations away from the mean with the remaining areas smaller than 1.87. C) z2 =-2.45 because the bigger z-value has a bigger area between -2.45 and 2.45. D) z1 =-1.87 because the area between -1.87 and 1.87 is smaller.
B)z2 =-2.45 because the z-value indicates almost two and a half standard deviations away from the mean with the remaining areas smaller than 1.87.
A researcher is wondering whether the smoking habits of young adults (18-25 years of age) in a certain city in the U.S. are the same as the proportion of the general population of young adults in the U.S. A recent study stated that the proportion of young adults who reported smoking at least twice a week or more in the last month was 0.16. The researcher collected data from a random sample of 75 adults in the city of interest. *A researcher completes a hypothesis test with a resulting p-value = 0.076. Choose the best statement to interpret the results A) The p-value for a two-sided test is divided by 2 resulting in a value less than a standard cutoff value of ΅ = 0.05 supporting the hypothesis that the city of interest has a different proportion of smokers than the general public. B)The p-value is above a standard cutoff value of ΅ = 0.05 and therefore there is sufficient evidence to support that the city of interest has a different proportion of smokers than the general public. C)The p-value is above a standard cutoff value of ΅ = 0.05 and therefore there is insufficient evidence to support that the city of interest has a different proportion of smokers than the general public. D)The standard cutoff value of ΅ = 0.05 is multiplied by two for a two-sided test and the resulting value of 0.10 is greater than the p-value. Therefore there is no evidence to support that the city of interest has a different proportion of smokers than the general public.
C)The p-value is above a standard cutoff value of ΅ = 0.05 and therefore there is insufficient evidence to support that the city of interest has a different proportion of smokers than the general public.
From the TI-84 graphing calculator screenshots below, there are specific shaded areas that represent p-values. Choose the statement that best describes the interpretation of these p-values. *graphs* A) The p-value shown in graphic c displays a small two-sided p-value. B) The p-value shown in graphic b displays a one-sided test with a small p-value. C)The p-values shown in graphics a and b display one-sided tests while c displays a shaded area showing a two-sided p-value. D) The p-value shown in graphic c displays a one-sided test with a small p-value
C)The p-values shown in graphics a and b display one-sided tests while c displays a shaded area showing a two-sided p-value.
(MC) A researcher wants to know whether athletic women are more flexible than non-athletic women. For this experiment, a woman who exercised vigorously at least four times per week was considered "athletic." Flexibility is measured in inches on a sit & reach box. Test the researcher's claim using the following summary statistics: Assume that all conditions for testing have been met. Report the test statistic and p-value. At the 1% significance level, state your decision regarding the null hypothesis and your conclusion about the original claim. Round all values to the nearest thousandth. A) t =1.623; p = 0.108; Reject the null hypothesis; there is not strong evidence to suggest that athletic women are more flexible than non-athletic women. B)t = -1.623; p = 0.054; Reject the null hypothesis; there is strong evidence to suggest that athletic women are more flexible than non-athletic women. C)t =1.623; p = 0.054; Fail to reject the null hypothesis; there is not strong evidence to suggest that athletic women are more flexible than non-athletic women. D)t = -1.623; p = 0.108; Reject the null hypothesis; there is strong evidence to suggest that athletic women are more flexible than non-athletic women.
C)t =1.623; p = 0.054; Fail to reject the null hypothesis; there is not strong evidence to suggest that athletic women are more flexible than non-athletic women.
A researcher believes that children who attend elementary school in a rural setting have lower obesity rates then children who attend elementary school in an urban setting. The researcher collects a random sample from each population and records the proportion of children in each sample who are clinically obese. The data is summarized in the table below. Assume that all conditions for proceeding with a two-sample test have been met. *Find the z-statistic (rounded to the nearest hundredth) and p-value (rounded to the nearest thousandth) for this hypothesis test. Using a 5% significance level, state the correct conclusion regarding the null hypothesis H0: prural = purban. A) z = -1.85, p = 0.032. There is sufficient evidence to accept the null hypothesis. B) z = -1.95, p = 0.026. There is not sufficient evidence to reject the null hypothesis. C)z =1.95, p = 0.026. There is sufficient evidence to prove that the population proportions are the same. D) z = -1.95, p = 0.026. There is sufficient evidence to reject the null hypothesis.
C)z =1.95, p = 0.026. There is sufficient evidence to prove that the population proportions are the same.
(MC) Choose the statement that describes a situation where a confidence interval and a hypothesis test would yield the same results. I. When the null hypothesis contains a population parameter that is equal to zero. II. When the alternative hypothesis is two-tailed. A) I and II B) I only C) II only D)Neither I nor II. The confidence interval cannot yield results that are the same as the hypothesis test.
C) II only
(Solve the Problem) A polling agency is interested in testing whether the proportion of women who support a female candidate for office is greater than the proportion of men. The null hypothesis is that there is no difference in the proportion of men and women who support the female candidate. The alternative hypothesis is that the proportion of women who support the female candidate is greater than the proportion of men. The test results in a p-value of 0.112. Which of the following is the best interpretation of the p-value? A) The p-value is the probability that men will support the female candidate. B) The p-value is the probability of getting a result that is as extreme as or more extreme than the one obtained, assuming that the proportion of women who support the female candidate is greater than the proportion of men. C) The p-value is the probability of getting a result that is as extreme as or more extreme than the one obtained, assuming that there is no difference in the proportions. D) The p-value is the probability that women will support the female candidate.
C) The p-value is the probability of getting a result that is as extreme as or more extreme than the one obtained, assuming that there is no difference in the proportions.
A research firm carried out a hypothesis test on a population proportion using a left-tailed alternative hypothesis. Which of the following z-scores would be associated with a p-value of 0.04? Round to the nearest hundredth. A) z = -2.50 B) z = 2.50 C) z = -1.75 D) z = 1.75
C) z = -1.75
Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim. *An entomologist writes an article in a scientific journal which claims that fewer than 8 in ten thousand male fireflies are unable to produce light due to a genetic mutation. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms. A) There is sufficient evidence to support the claim that the true proportion is greater than 8 in ten thousand. B)There is not sufficient evidence to support the claim that the true proportion is greater than 8 in ten thousand. C)There is sufficient evidence to support the claim that the true proportion is less than 8 in ten thousand. D)There is not sufficient evidence to support the claim that the true proportion is less than 8 in ten thousand.
C)There is sufficient evidence to support the claim that the true proportion is less than 8 in ten thousand.
A researcher is wondering whether the drinking habits of adults in a certain region of the country are in the same proportion as the general population of adults. Suppose a recent study stated that the proportion of adults in the general population who reported drinking once a week or less in the last month was 0.26. The null hypothesis for this test is H0: p = 0.26 and the alternative hypothesis is Ha: p < 0.26. The researcher collected data from 150 surveys he handed out at a busy park located in the region. *Check that the conditions hold so that the sampling distribution of the z-statistic will approximately follow the standard Normal distribution. Are the conditions satisfied? If not, choose the condition that is not satisfied. A) Yes, all the conditions are satisfied. B) No, the population of interest is not large enough to assume independence. C) Yes, the population of proportions can be assumed to be roughly symmetric. D) No the conditions are not satisfied; the researcher did not collect a random sample.
D) No the conditions are not satisfied; the researcher did not collect a random sample.
Solve the problem. *A quality control manager thinks that there is a higher defective rate on the production line than the advertised value of p = 0.025. She does a hypothesis test with a significance level of 0.05. Symbolically, the null and alternative hypothesis are as follows: H0: p = 0.025 and Ha: p > 0.025. She calculates a p-value for the hypothesis test of defective light bulbs to be approximately 0.067. Choose the correct interpretation for the p-value. A) The p-value tells us that the result is significantly higher than the advertised value using a significance level of 0.05. B)The p-value tells us that the probability of concluding that the defect rate is equal to 0.025, when in fact it is greater than 0.025, is approximately 0.067. C)The p-value tells us that the true population rate of defective light bulbs is approximately 0.067. D)The p-value tells us that if the defect rate is 0.025, then the probability that she would observe the percentage she actually observed or higher is 0.067. At a significance level of 0.05, this would not be an unusual outcome.
D)The p-value tells us that if the defect rate is 0.025, then the probability that she would observe the percentage she actually observed or higher is 0.067. At a significance level of 0.05, this would not be an unusual outcome.
(MULTIPLE CHOICE) Suppose a consumer product researcher wanted to find out whether a highlighter lasted longer than the manufacturer's claim that their highlighters could write continuously for 14 hours. The researcher tested 40 highlighters and recorded the number of continuous hours each highlighter wrote before drying up. Test the hypothesis that the highlighters wrote for more than 14 continuous hours. Following are the summary statistics: x =14.5 hours, s =1.2 hours Report the test statistic, p-value, your decision regarding the null hypothesis. At the 5% significance level, state your conclusion about the original claim. Round all values to the nearest thousandth. A)t = 2.635; p = 0.006; Fail to reject the null hypothesis; there is not strong evidence to suggest that the highlighters last longer than 14 hours. B)t = 2.635; p = 0.006; Reject the null hypothesis; there is strong evidence to suggest that the highlighters last longer than 14 hours. C)z = 9.583; p = 0.000+; Reject the null hypothesis; there is strong evidence to suggest that the highlighters last longer than 14 hours. D)z = 9.583; p = 0.000+; Fail to reject the null hypothesis; there is not strong evidence to suggest that the highlighters last longer than 14 hours.
. B)t = 2.635; p = 0.006; Reject the null hypothesis; there is strong evidence to suggest that the highlighters last longer than 14 hours.
Use the following information to answer the question. A janitor at a large office building believes that his supply of light bulbs has too many defective bulbs. The janitor's null hypothesis is that the supply of light bulbs has a defect rate of p = 0.07 (the light bulb manufacturer's stated defect rate). Suppose he does a hypothesis test with a significance level of 0.05. Symbolically, the null and alternative hypothesis are as follows: H0: p = 0.07 and Ha: p > 0.07. *Choose the statement that best describes the significance level in the context of the hypothesis test. A) The significance level of 0.05 is the test statistic that we will use to compare the observed outcome to the null hypothesis. B) The significance level of 0.05 is the probability of concluding that the defect rate is higher than 0.07 when in fact the defect rate is equal to 0.07. C) The significance level of 0.05 is the defect rate we believe is the true defect rate. D) The significance level of 0.05 is the probability of concluding that the defect rate is equal to 0.07 when in fact it is greater than 0.07.
B) The significance level of 0.05 is the probability of concluding that the defect rate is higher than 0.07 when in fact the defect rate is equal to 0.07.
A statistics student has heard that about 26% of the students on his campus attend sporting events weekly. He wants to know if statistics students attend events in the same proportions as the general student body. Explain what the second type of error would be in this case (where the student fails to reject a null hypothesis that is actually false). A) The second kind of error would be saying that statistics students attend sporting events in much higher proportions than the student body as a whole, even though they actually have the same attendence proportion. B)The second kind of error would be saying that there is no difference in the attendence of statistics students and the student body as a whole at sporting events, even though statistics students actually go much less often. C)The second kind of error would be saying that statistics students attend sporting events in different proportions than the student body as a whole, even though they actually have the same attendance proportion. D)The second kind of error would be saying that there is no difference in the attendance of statistics students and the student body as a whole at sporting events, even though there really is.
. D)The second kind of error would be saying that there is no difference in the attendance of statistics students and the student body as a whole at sporting events, even though there really is.
(MC) An economist conducted a hypothesis test to test the claim that the average cost of eating a meal at home increased from 2009 to 2010. The average cost of eating a meal at home in 2009 was $5.25 per person per meal. Assume that all conditions for testing have been met. He used technology to complete the hypothesis test. Following is his null and alternative hypothesis and the output from his graphing calculator. H0: µ = $5.25 Ha: µ > $5.25 At the 5% significance level, choose the statement that contains the correct conclusion regarding the hypothesis and the original claim A) Reject the null hypothesis; there is sufficient evidence to support the claim that the average cost of eating at home has increased since 2009. B)Fail to reject the null hypothesis; there is sufficient evidence to support the claim that the average cost of eating at home has increased since 2009. C)Fail to reject the null hypothesis; there is not sufficient evidence to support the claim that the average cost of eating at home has increased since 2009. D)Reject the null hypothesis; there is not sufficient evidence to support the claim that the average cost of eating at home has increased since 2009
A) Reject the null hypothesis; there is sufficient evidence to support the claim that the average cost of eating at home has increased since 2009.
Use the following information to answer the question. A researcher is wondering whether the drinking habits of adults in a certain region of the country are in the same proportion as the general population of adults. Suppose a recent study stated that the proportion of adults who reported drinking once a week or less in the last month was 0.26. The researcher's null hypothesis for this test is H0: p = 0.26 and the alternative hypothesis is Ha: p > 0.26. The researcher collected data from a random sample of 75 adults in the region of interest. *Check that the conditions hold so that the sampling distribution of the z-statistic will approximately follow the standard normal distribution. Are the conditions satisfied? If not, choose the condition that is not satisfied. A) Yes, all the conditions are satisfied. B) No, the population of interest is not large enough to assume independence. C) No, the researcher did not collect a random sample. D) No, the researcher did not collect a large enough sample
A) Yes, all the conditions are satisfied.
Use the following information to answer the question. A janitor at a large office building believes that his supply of light bulbs has too many defective bulbs. The janitor's null hypothesis is that the supply of light bulbs has a defect rate of p = 0.07 (the light bulb manufacturer's stated defect rate). Suppose he does a hypothesis test with a significance level of 0.05. Symbolically, the null and alternative hypothesis are as follows: H0: p = 0.07 and Ha: p > 0.07. *The janitor calculates a p-value for the hypothesis test of approximately 0.087. Choose the correct interpretation for the p-value. A) The p-value tells us that the probability of concluding that the defect rate is equal to 0.07, when in fact it is greater than 0.07, is approximately 0.087. B) The p-value tells us that if the defect rate is 0.07, then the probability that the janitor will have 27 defective light bulbs out of 300 is approximately 0.087. At a significance level of 0.05, this would not be an unusual outcome. C) The p-value tells us that the true population rate of defective light bulbs is approximately 0.087. D) None of these
B) The p-value tells us that if the defect rate is 0.07, then the probability that the janitor will have 27 defective light bulbs out of 300 is approximately 0.087. At a significance level of 0.05, this would not be an unusual outcome.
(mc) A researcher wants to know if mood is affected by music. She conducts a test on a sample of 4 randomly selected adults and measures mood rating before and after being exposed to classical music. Test the hypothesis that mood rating improved after being exposed to classical music. Following are the mood ratings for the four participants: Assume that all conditions for testing have been met. Report the null and alternative hypothesis and p-value. At the 5% significance level, state your decision regarding the null hypothesis and your conclusion about the original claim. Round all values to the nearest thousandth. A)H0: µ1 = µ2, Ha: µ1 < µ2; p = 0.077; Fail to reject the null hypothesis; there is not strong evidence to suggest that exposure to classical music improved mood rating. B)H0: µdifference = 0, Ha: µdifference < 0; p = 0.008; Reject the null hypothesis; there is strong evidence to suggest that exposure to classical music improved mood rating. C)H0: µ1 = µ2, Ha: µ1 J µ2; p = 0.008; Fail to reject the null hypothesis; there is not strong evidence to suggest that exposure to classical music improved mood rating. D)H0: µdifference = 0, Ha: µdifference > 0; p = 0.922; Fail to reject the null hypothesis; there is not strong evidence to suggest that exposure to classical music improved mood rating.
B)H0: µdifference = 0, Ha: µdifference < 0; p = 0.008; Reject the null hypothesis; there is strong evidence to suggest that exposure to classical music improved mood rating.
A quality control manager believes that there are too many defective light bulbs being produced, higher than the advertised rate. The manager's null hypothesis is that the production line of light bulbs has a defect rate of p = 0.025 (the light bulb's stated defect rate). He does a hypothesis test with a significance level of 0.05. Symbolically, the null and alternative hypothesis are as follows: H0: p = 0.025 and Ha : p > 0.025. *Choose the statement that best describes the significance level in the context of the hypothesis test A) The significance level of 0.05 is the probability of concluding that the defect rate is equal to 0.025 when in fact it is greater than 0.025. B) The significance level of 0.05 is the defect rate we believe is the true defect rate. C)The significance level of 0.05 is the test statistic that we will use to compare the observed outcome to the null hypothesis. D)The significance level of 0.05 is the probability of concluding that the defect rate is higher than 0.025 when in fact the defect rate is equal to 0.025.
D)The significance level of 0.05 is the probability of concluding that the defect rate is higher than 0.025 when in fact the defect rate is equal to 0.025.
Solve the problem. *A researcher conducts a hypothesis test on a population proportion. Her null and alternative hypothesis are H0: p = 0.6 and Ha : p < 0.6 . The test statistic and p-value for the test are z =ȱƺ1.51 and pƺvalue = 0.0655. For a significance level of ΅ = 0.05, choose the correct conclusion regarding the null hypothesis A) There is sufficient evidence to conclude that the population proportion is significantly different from 0.6. B)There is sufficient evidence to accept the null hypothesis that the population proportion is equal to 0.6. C) There is insufficient evident to determine the significance. D)There is insufficient evidence to reject the null hypothesis that the population proportion is equal to 0.6.
D)There is insufficient evidence to reject the null hypothesis that the population proportion is equal to 0.6.
An economist conducted a hypothesis test to test the claim that the average cost of eating a meal 39) away from home decreased from 2009 to 2010. The average cost of eating a meal away from home in 2009 was $7.15 per person per meal. Assume that all conditions for testing have been met. He used technology to complete the hypothesis test. Following is his null and alternative hypothesis and the output from his graphing calculator. H0: μ = $7.15 Ha: μ < $7.15 *Choose the statement that contains the correct conclusion regarding the hypothesis and the original claim. A) Fail to reject the null hypothesis; there is sufficient evidence to support the claim that the average cost of eating away from home has decreased since 2009. B) Fail to reject the null hypothesis; there is not sufficient evidence to support the claim that the average cost of eating away from home has decreased since 2009. C) Reject the null hypothesis; there is sufficient evidence to support the claim that the average cost of eating away from home has decreased since 2009. D) Reject the null hypothesis; there is not sufficient evidence to support the claim that the average cost of eating away from home has decreased since 2009.
B) Fail to reject the null hypothesis; there is not sufficient evidence to support the claim that the average cost of eating away from home has decreased since 2009.
(MC) A researcher wants to know whether athletic men are more flexible than non-athletic men. For this experiment, a man who exercised vigorously at least four times per week was considered "athletic". Flexibility is measured in inches on a sit & reach box. Test the researcher's claim using the following summary statistics: Assume that all conditions for testing have been met. Report the test statistic and p-value. At the 5% significance level, state your decision regarding the null hypothesis and your conclusion about the original claim. Round all values to the nearest thousandth A)t =-3.270; p = 0.002 ; Reject the null hypothesis; there is strong evidence to suggest that athletic men are more flexible than non-athletic men. B)t = 3.270; p = 0.001 ; Reject the null hypothesis; there is strong evidence to suggest that athletic men are more flexible than non-athletic men. C)t =-3.270; p = 0.002 ; Reject the null hypothesis; there is not strong evidence to suggest that athletic men are more flexible than non-athletic men. D)t = 3.270; p = 0.001 ; Fail to reject the null hypothesis; there is not strong evidence to suggest that athletic men are more flexible than non-athletic men.
B)t = 3.270; p = 0.001 ; Reject the null hypothesis; there is strong evidence to suggest that athletic men are more flexible than non-athletic men.
Use the following information to answer the question. A researcher is wondering whether the drinking habits of adults in a certain region of the country are in the same proportion as the general population of adults. Suppose a recent study stated that the proportion of adults who reported drinking once a week or less in the last month was 0.26. The researcher's null hypothesis for this test is H0: p = 0.26 and the alternative hypothesis is Ha: p > 0.26. The researcher collected data from a random sample of 75 adults in the region of interest. ^ *To continue the study into the drinking habits of adults, the researcher decides to collect data from adults working in "blue collar" jobs to see whether their drinking habits are in the same proportion as the general public. The null hypothesis for this test is H0: p = 0.26 and the alternative hypothesis is Ha: p > 0.26. The researcher collected data from a random sample of 90 adults with "blue collar" jobs of which 30 stated that they drank once a week or less in the last month. Assume that the conditions that must be met in order for us to use the N(0, 1) distribution as the sampling distribution are satisfied. Find the values of the sample proportion, p, the test statistic, and the p-value associated with the test statistic. Round all values to the nearest thousandth. A) ^ p = 0.333, z = 1.586, p-value = 0.056 B) ^p = 0.289, z = -0.829, p-value = 0.407 C) ^p = 0.333, z = 0.067, p-value = 0.946 D) ^p = 0.667, z = 8.795, p-value = 0.000
A) ^ p = 0.333, z = 1.586, p-value = 0.056
A janitor at a large office building believes that his supply of light bulbs has a defect rate that is higher than the defect rate stated by the manufacturer. The janitor's null hypothesis is that the supply of light bulbs has a manufacturer's defect rate of p = 0.09. He performs a test at a significance level of 0.01. The null and alternative hypothesis are as follows: H0: p = 0.09 and Ha: p > 0.09. *Suppose the janitor tests 300 light bulbs and finds that 33 bulbs are defective. The calculated test 6) statistic is z = 1.21. Select the appropriate interpretation of the test statistic. A) A test statistic of 1.21 is 1.21 standard deviations less than the mean (between 1 and 2) indicating that the result is not significant. B) A test statistic of 1.21 is 1.21 standard deviations greater than the mean (between 1 and 2) indicating that the result is not significant at a level of 0.01 using a one-sided alternative hypothesis. C) A test statistic of -1.21 is 1.21 standard deviations less than the mean (between 1 and 2) indicating that the result could be significant at a level of 0.01 using a one-sided alternative hypothesis. D) A test statistic of 1.21 is 1.21 standard deviations greater than the mean (between 1 and 2) indicating that the result could be significant using a two-sided alternative hypothesis.
B) A test statistic of 1.21 is 1.21 standard deviations greater than the mean (between 1 and 2) indicating that the result is not significant at a level of 0.01 using a one-sided alternative hypothesis.
Which of the following is not true about the alternative hypothesis? A) It is sometimes called the research hypothesis. B) Like the null hypothesis, it is always a statement about a population parameter. C) It is assumed to be true. D) It is usually a statement that the researcher hopes to demonstrate is true.
C) It is assumed to be true.
Two movie reviewers give movies "thumbs up" and "thumbs down" ratings. You sample 100 movies that they both have rated and find that they both gave "thumbs up" to 25 movies, both gave "thumbs down" to 30 movies, Sarah gave "thumbs up" and Jessica "thumb down" to 28 movies, and the remaining movies Sarah gave "thumbs down" and Jessica "thumbs up". Test whether there is a tendency for one reviewer to give more movies "thumbs up" (proportion 1) than the other (proportion 2). A) z = 1.96 There is sufficient evidence to accept the null hypothesis. B) z =-1.96 There is sufficient evidence to reject the null hypothesis. C)z = 1.56; For a two-sided test at D = 0.05 level, there is insufficient evidence to reject the null hypothesis because the cutoff z-value is at 1.96. D)z =-1.56; For a two-sided test at D = 0.05 level, there is insufficient evidence to reject the null hypothesis because the cutoff z-value is at 1.96.
D)z =-1.56; For a two-sided test at D = 0.05 level, there is insufficient evidence to reject the null hypothesis because the cutoff z-value is at 1.96.
(SHORT ANSWER) A sociologist believes that the proportion of single men who attend church on a regular basis is less than the proportion of single women. She takes a random sample from each population and records the proportion from each that reported that they attended church on a regular basis. The null hypothesis is H0: pmen = pwomen. State the correct alternative hypothesis with a sentence and symbolically.
hO: PMEN=PWOMEN hA: PMEN<PWOMEN
