A plan for an executive travelers' club has been developed by an airline on the premise that 5% of its current customers would qualify for membership. A random sample of 500 customers yielded 40 who would qualify.
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- A record store owner finds that 15,0% of customers entering her store make a purchase. One morning 188 people, who can be regarded a random sample of all customers, enter the store. What is the standard error of the sample proportion of customers making a purchase?From the U.S. Census Bureau’s American Community Survey in 2019 it was found that 33.13%of United States residents over the age of 25 had an educational attainment of a bachelor’sdegree or higher. In the District of Columbia, the percentage of residents over the age of 25 whohad attained a bachelor’s degree or higher was 59.67%. An investigator for the U.S. CensusBureau took a random sample of seven residents from the District of Columbia and asked themtheir highest educational degree they had obtained. a) Verify that the sample from the District of Columbia satisfies the conditions of thebinomial experiment. Write one sentence to check each requirement in context of theinvestigation.b) Assuming the sample from the District of Columbia is a binomial experiment, build theprobability distribution in a single table and include the table in your solutions. You maypresent this table horizontally or vertically and leave the probabilities unrounded. Thereare two possible ways to do this: To…According to the National Institute on Alcohol Abuse and Alcoholism (NIAAA), and the National Institutes of Health (NIH), 42% of college students nationwide engage in “binge drinking” behavior, having 5 or more drinks in one occasion during the past two weeks. A college president wonders if the proportion of students enrolled at her college that binge drink is actually different than the national proportion. In a commissioned study, 364 students are selected randomly from a list of all students enrolled at the college. Of these, 136 admitted to having engaged in binge drinking. The same college president is more interested in testing her suspicion that the proportion of students at her college that binge drink is different than the national proportion of .37. Use the statistic provided for her college above for your test. A. Define the null and alternative hypotheses to test this claim. B. By hand, calculate the test statistic for this test. C. Use…
- As products come off a large assembly line, they are inspected for quality. They are placed into one of three categories: pass, fail, or need additional inspection. The manager claims that 80% of the products pass the inspection, 5% fail, and 15% need additional inspection. In an effort to increase the passing rate, the machines are recalibrated. After this recalibration, a random sample of 100 products is selected. It is discovered that 85 passed inspection, 2 failed, and 13 needed additional inspection. The manager would like to know if there is convincing evidence that the distribution has changed. What is the value of the chi-square test statistic and P-value? Find the chi-square table here. χ2 = 2.38, P-value is less than 0.0005 χ2 = 2.38, P-value is greater than 0.25 χ2 = 5.10, P-value is less than 0.0005 χ2 = 5.10, P-value is greater than 0.25For several decades, it was a common practice in Southern California for houses to be built with pools in the backyard (as any airplane flight which ends at a Southern California airport will reveal). Now, however, that practice may be changing, possibly because of the recent demand for landscaped homes, which experts believe help reduce pollution. A recent study examined a random sample of 167 houses built in Southern California between 1950 and 1985 and an independent, random sample of 80 houses built in Southern California from 1992 to the present. The sample of houses built in 1950-1985 contained 71 houses with pools, and the sample of houses built from 1992-present contained 31 houses with pools. Based on this survey, can we conclude, at the 0.05 level of significance, that the proportion p1 of all Southern California houses built in 1950-1985 that were built with pools is greater than the proportion p2 of all Southern California houses built from…It is believed that 11% of all Americans are left-handed. A college needs to know how many left-handed desks to place in the big lecture halls being constructed on its campus. In a random sample of 210 students from that college, whether or not a student was left-handed was recorded for each student. The college wants to know if the data provide enough evidence to show that students at this college have a different percentage of left-handers than the general American population? State the random variable, population parameter, and hypotheses. State the Type I and Type II errors in the context of this problem.a) The symbol for the random variable involved in this problem is The wording for the random variable in context is as follows: b) The symbol for the parameter involved in this problem is The wording for the parameter in context is as follows: c) Fill in the correct null and alternative hypotheses: H0:H0: HA:HA:…
- Fewer young people are driving. In 1995, 63.9% of people under 20 years old who were eligible had a driver's license. Bloomberg reported that percentage had dropped to 41.7% in 2016. Suppose these results are based on a random sample of 1,200 people under 20 years old who were eligible to have a driver's license in 1995 and again in 2016.According to the National Institute on Alcohol Abuse and Alcoholism (NIAAA) and the National Institutes of Health (NIH), 41% of college students nationwide engage in "binge-drinking" behavior: having five or more drinks on one occasion during the past two weeks. A college president wonders if the proportion of students enrolled at her college who binge drink is actually lower than the national proportion. In a commissioned study, 346 students are selected randomly from a list of all students enrolled at the college. Of these, 135 admit to having engaged in binge drinking.The college president is more interested in testing her belief that the proportion of students at her college who engage in binge drinking is lower than the national proportion of 0.41. What is the P-value? (Round your answer to four decimal places.) P-value =A market research group is interested in estimating the market share of three airline companies, A, B and C, operating on a particular flight path. These three airlines are the only companies operating on this route. Airline B claim that they have 50% of the business with the remaining percentage shared equally amongst airlines A and C, i.e. 25% each. The market research group decide to carry out an independent study and question a random sample of 97 people visiting an airport on a particular day. Each person was given price, timetables and service details of flights on this route for each of the three airlines. Provided with this information they were asked to select their airline of choice.The survey revealed the following observed frequencies Airline A - 26 Aurline B - 49 Airline C - 22 Test if there is any evidence to suggest that the airline's claim is incorrect, at significance level α = 0.05. Complete the test by answering the following questions : Which of the following is the…
- According to the National Institute on Alcohol Abuse and Alcoholism (NIAAA), and the National Institutes of Health (NIH), 42% of college students nationwide engage in “binge drinking” behavior, having 5 or more drinks in one occasion during the past two weeks. A college president wonders if the proportion of students enrolled at her college that binge drink is actually different than the national proportion. In a commissioned study, 364 students are selected randomly from a list of all students enrolled at the college. Of these, 136 admitted to having engaged in binge drinking. Calculate the statistic for this sample. Calculate the standard error for this sample. Verify that we can use a normal distribution for this sample. By hand calculate a 90% confidence interval for the proportion of all students at this college that engage in binge drinking. Show all work. Interpret the results of your confidence interval in the context of the…In a survey of 1,000 women aged 22 to 35 who work full time, 555 indicated that they would be willing to give up some personal time in order to make more money. The sample was selected in a way that was designed to produce a sample that was representative of women in the targeted age group. (a) Do the sample data provide convincing evidence that the majority of women aged 22 to 35 who work full-time would be willing to give up some personal time for more money? Test the relevant hypotheses using ? = 0.01. Find the test statistic and P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z = P-value = (B ) State your conclusion. a. Fail to reject H0. We have convincing evidence that a majority of women aged 22 to 35 who work full time would be willing to give up some personal time for more money. b. Fail to reject H0. We do not have convincing evidence that a majority of women aged 22 to 35 who work full…A local school board wants to estimate the difference in the proportion of households with school-aged children that would support starting the school year a week earlier, and the proportion of households without school-aged children that would support starting the school year a week earlier. They survey a random sample of 40 households with school-aged children about whether they would support starting the school year a week earlier, and 30 households respond yes. They survey a random sample of 45 households that do not have school-aged children, and 25 respond yes. Assuming the conditions for inference have been met, what is the 90% confidence interval for the difference in proportions of households that would support starting the school year a week earlier? Find the z-table here. 0.75(1-0.75), 0.56(1-0.56) O (0.75 - 0.56) ±1.65 45 40 0.75(1-0.75) 0.56(1-0.56) O (0.75 - 0.56) ±1.96, 85 85 O (0.75 - 0.56) ±1.65, 0.75(1-0.75) 0.56(1-0.56) + 40 45 O (0.75 - 0.56) ±1.96 0.75(1-0.75)…