A MANUFACTURER CLAIMS THAT ONLY 4% OF HIS PRODUCTS ARE DEFECTIVE. A RANDOM SAMPLE OF 500 WAS TAKEN AMONG WHICH 100 DEFECTIVE. TEST THE HYPOTHESIS AT 0.05 LEVELS.
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![A MANUFACTURER CLAIMS THAT ONLY 4% OF HIS PRODUCTS ARE
DEFECTIVE. A RANDOM SAMPLE OF 500 WAS TAKEN AMONG WHICH
100 DEFECTIVE. TEST THE HYPOTHESIS AT 0.05 LEVELS.
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- A new screening test for Lyme disease is developed for use in the general population. The sensitivity and specificity of the new test are 60% and 70%, respectively. Five hundred people are screened at a clinic during the first year the new test is implemented. Assume the true prevalence of Lyme disease among clinic attendees is 10%. Calculate the predictive value of a positive test.Suppose we want to know if the proportion of people with a certain trait is less than 0.5. We observe 100 people and find that 44 of them have the trait of interest. Assume that the samples are Normally distributed. Conduct a hypothesis test at level 0.05 using a p-value to answer this question.A sociologist is studying the age of the population in Blue Valley. Ten years ago, the population was such that 19% were under 20 years old, 14% were in the 20- to 35-year-old bracket, 33% were between 36 and 50, 23% were between 51 and 65, and 11% were over 65. A study done this year used a random sample of 210 residents. This sample is given below. At the 0.01 level of significance, has the age distribution of the population of Blue Valley changed?Under 20 20 - 35 36 - 50 51 - 65 Over 6529 27 67 65 22(i) Give the value of the level of significance. State the null and alternate hypotheses.H0: The population 10 years ago and the population today are independent.H1: The population 10 years ago and the population today are not independent.H0: The distributions for the population 10 years ago and the population today are the same.H1: The distributions for the population 10 years ago and the population today are different. H0: Time ten years ago and today are independent.H1: Time ten years…
- In a survey of 180 females who recently completed high school, 75% were enrolled in college. In a survey of 160 males who recently completed high school,70 % were enrolled in college. At a=.009, can you reject the claim that there is no difference in the proportion of college enrollees between the two groups? Assume the random samples are independent. Complete parts (a) through (e).Citrus Rental is a popular car rental agency that has a history of having too few cars available, so that its available cars are overdriven. The mean monthly mileage over the years for Citrus cars has been about 1550 miles per month. Recently, though, Citrus purchased thousands of new cars, and the company claims that the average mileage of its cars is now less than in the past. To test this, a random sample of 13 recent mileages of Citrus cars was taken. The mean of these 13 mileages was 1425 miles per month, and the standard deviation was 209 miles per month. Assume that the population of recent monthly mileages of Citrus cars is normally distributed. At the 0.10 level of significance, can it be concluded that the mean recent monthly mileage, μ, of Citrus cars is less than 1550 miles per month? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (If necessary,…In 1965, about 44% of the u.s. adult population had never smoked cigarettes. A national health survey of 1360 u.s adults(selected randomly) during 2020 revealed that 626 had never smoked cigarettes. Using a=0.05, test whether there has been a change since 1965 in the proportion of u.s. adults that have never smoked cigarettes. State the hypothesis, list and check the conditions, calculate the test statistic, find the p-value, and make a conclusion in a complete sentence related to the scenario
- Data from the Department of Motor Vehicles indicate that 80% of all licensed drivers are older than age 25. In a sample of n = 50 people who recently received speeding tickets, 33 were older than age 25 and the other 17 were age 25 or younger. Is the age distribution for this sample significantly different from the distribution for the population of licensed drivers? Use alpha = .05. In a sample of n = 50 people who recently received parking tickets, 36 were older than age 25 and the other 14 were age 25 or younger. Is the age distribution for this sample significantly different from the distribution for the population of licensed drivers? Use alpha = .05.You are interested in testing if more than 46% of registered voters will vote for your preferred candidate in the next election. You managed to obtain a sample of 530 registered voters; 264 plan to vote for your candidate. Conduct the test and calculate and interpret the p-value; alpha is not provided.Prior to an intensive TV advertising campaign, the producers of Nike athletic shoes find that 29 of a random sample of 200 upper-income adults are aware of their new leisure shoe line. A second random sample of 300 such adults is taken after the campaign. Now 96 of the persons sampled can identify the new line. Is the increase in the proportion of upper income adults showing brand awareness significant? Test the claim using alpha = .05.
- Citrus Rental is a popular car rental agency that has a history of having too few cars available, so that its available cars are overdriven. The mean monthly mileage over the years for Citrus cars has been about 1600 miles per month. Recently, though, Citrus purchased thousands of new cars, and the company claims that the average mileage of its cars is now less than in the past. To test this, a random sample of 16 recent mileages of Citrus cars was taken. The mean of these 16 mileages was 1517 miles per month, and the standard deviation was 233 miles per month. Assume that the population of recent monthly mileages of Citrus cars is normally distributed. At the 0.05 level of significance, can it be concluded that the mean recent monthly mileage, μ, of Citrus cars is less than 1600 miles per month? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (If necessary,…The school registrar estimates that the dropout rate of freshmen high schools in Valenzuela is 20%. Last year, 90 freshmen from a random sample of 500 Valenzuela freshmen high school withdrew. At 0.01, is there enough evidence to reject the registrar's claim?An educator believes that the proportion of finance majors seeking to earn an MBA degree equals the proportion of management majors seeking to earn an MBA degree in the population. A random sample of 100 finance majors is taken and 24 indicate that they will seek to earn an MBA degree. Likewise, a random sample of 400 management majors is taken and 65 indicate that they will seek to earn an MBA degree. Using this information, test the educator’s claim at the 0.05 level
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