A market researcherbelieves that in a certain population the proportion of persons preferring brands A, B, C, and D of tooth paste are 0.20, 0.70, 0.02 and 0.08 respectively. A simple random sample of 600 persons drawn from the population shows the following preference. Brand A B D Number of person 190 344 44 22 Do these data provide sufficient evidence to reject the researcher's belief at a = 0.01
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- 7. 40% of consumers believe that cash will be obsolete in the next 20 years based on a survey by J.P. Morgan Chase. Eight consumers are randomly selected and the number who believe cash will be obsolete is recorded. X 0 1 2 3 4 5 6 7 8 P(x) 0.017 0.090 0.209 0.124 0.041 0.008 0.001 Fill in the missing values from the table and identify each of the following characteristics used to construct the distribution: n= p= Discuss the three characteristics of the distribution. Shape: Center: Spread: Find the probability that exactly 4 people believe that cash will be obsolete. Find the probability that between 3 and 7 people believe that cash will be obsolete. Find the probability that at most 3 people believe that cash will be obsolete. x=A study is conducted in a large high school to determine if the proportion of students who plan to come to the upcoming football game differs across the grades. A random sample of 50 ninth graders, 50 tenth graders, 50 eleventh graders, and 50 twelfth graders was selected. The responses are displayed in the table. The principal would like to know if these data provide convincing evidence that the distribution of responses differs across the grades in the population of all students in her school. The random and 10% conditions are met, and this table of expected counts shows that all expected counts are at least 5. What is the value of the chi-square test statistic for this test? χ‑2 = 0.49 χ‑2 = 0.70 χ‑2 = 0.84 χ‑2 = 200When two births are randomly selected, the sample space for genders is bb, bg. gb, and gg. Assume that those four outcomes are equally likely. Construct a table that describes the sampling distribution of the sample proportion of girls from two births. Does the mean of the sample proportions equal the proportion of girls in two births? Does the result suggest that a sample proportion an unbiased estimator of a population proportion? For the entire population, assume the probability of having a boy is the probability of having a girl is , and this is not affected by how many boys or girls have previously been born. 2 Determine the probabilities of each sample proportion. Probability Sample proportion of girls Tune intanare or cimnlifiad frartinne
- Suppose that Mairin has knit a collection of wool‑blend infinity scarves that she wants to sell in her Etsy shop for $28.00 each. However, she is worried that if the average price of comparable scarves is less than $28.00, hers would be less likely to sell. Mairin selected a random sample of 9 similar hand‑knit, wool‑blend infinity scarves, and their prices are as follows. $21.75,$24.00,$27.25,$29.95,$23.00,$26.00,$27.80,$33.50,$27.00$21.75,$24.00,$27.25,$29.95,$23.00,$26.00,$27.80,$33.50,$27.00 Use a left‑tailed one‑sample ?t‑test to determine whether the average price of hand‑knit, wool‑blend infinity scarves sold on Etsy is less than $28.00. Assume that the prices of all comparable scarves are normally distributed. Mairin should (reject, accept, fail to accept) her null hypothesis. There is (sufficient, no, insufficient) evidence that the mean price of hand‑knit, wool‑blend infinity scarves is (greater than, different from, less than, equal two) $28.00.A university wanted to see whether there was a significant difference in age between its day staff and evening staff. A random sample of 35 staff members is selected from each group. The data are given below. Test the hypothesis that there is no difference in age between the two groups. Use a =0.05. Day Staff 22 24 24 23 19 19 23 22 18 21 21 18 18 25 29 24 23 22 22 21 20 20 20 27 17 19 18 21 20 23 26 30 25 21 25 Evening Staff 18 23 25 23 21 21 23 24 27 31 24 20 20 23 19 25 24 27 23 20 20 21 25 24 23 28 20 19 23 24 20 27 21 29 307h. A travel association reported the domestic airfare (in dollars) for business travel for the current year and the previous year. Below is a sample of 12 flights with their domestic airfares shown for both years. CurrentYear PreviousYear 345 315 526 451 420 450 216 206 285 263 405 432 635 585 710 650 605 545 517 547 570 496 610 580 Calculate the test statistic. (Use current year airfare − previous year airfare. Round your answer to three decimal places.) Calculate the p-value. (Round your answer to four decimal places.) p-value =
- A regional transit authority is concerned about the number of riders on one of its bus routes. In setting up the route, the assumption is that the number of riders is the same on every day from Monday through Friday. A random sample of 100 riders yielded the following results: Day Monday Tuesday Wednesday Thursday Friday Using a = 10%, determine whether the transit authority's assumption is correct. Number of Riders 20 15 30 17 16The following table shows the ethnic origins of two random samples of students from a Canadian university, one from 2012 and the other from 2022: European 2012 2022 African Asian 308 58 52 364 100 58 Note: Canadian born students are classified according to their ancestry. (a) What would be an appropriate test to check if there has been an overall change in the distribution of ethnic origins among the student population of that university between 2012 and 2022? Justify your answer. ] Other 22 38 (b) Based on your answer in (a) above, test whether there has been an overall change in the distribution of ethnic origins among the student population of that university between 2012 and 2022. Use a 5% significance level and show your detailed manual calculations and all the steps of your hypothesis test (hypotheses, significance level, expected cell frequencies (rounded to 1 decimal), test statistic, decision criteria, critical value and p-value, conclusion with justification). (Manual…In testing a certain kind of truck tire over rugged terrain, it is found that 39% of the trucks fail to complete the test run without a blowout. Of the next 15 trucks tested, find the probability that at least 3 trucks have blowouts.
- A survey is conducted to determine if there is a difference in the proportion of students, parents, and What are the appropriate hypotheses to determine if the distribution of response differs among these three populations? teachers who volunteer at least once a month. To investigate, a random sample of 45 students, 25 parents, and 12 teachers was selected from a large high school. The data are displayed in the table. O Ho: There is a difference in the distribution of responses among these three populations. Hg: There is no difference in the distribution of Student Parent Teacher responses among these three populations. 12 O Ho: There is no difference in the distribution of Yes 24 Volunteer? responses among these three populations. Hg: There is a difference in the distribution of No 21 13 response among these three populations. Họ: There is no association between the type of person who is surveyed and the response. Hạ: There is an association between the type of person who is surveyed…A statistical test is conducted to see if there is evidence that the proportion of US citizens who can name the capital city of Mexico is less than 0.6. Use the following possible sample results: Sample A: 19 successes out of 40 Sample B: 22 successes out of 40 Sample C: 24 successes out of 40 Sample D: 26 successes out of 40 State which of the possible sample results provides the most significant evidence for the claim. Sample B Sample D Sample C Sample AA random sample of n1 = 10 regions in New England gave the following violent crime rates (per million population). x1: New England Crime Rate 3.3 3.7 4.2 3.9 3.3 4.1 1.8 4.8 2.9 3.1 Another random sample of n2 = 12 regions in the Rocky Mountain states gave the following violent crime rates (per million population). x2: Rocky Mountain Crime Rate 3.9 4.1 4.5 5.5 3.3 4.8 3.5 2.4 3.1 3.5 5.2 2.8 Assume that the crime rate distribution is approximately normal in both regions. Do the data indicate that the violent crime rate in the Rocky Mountain region is higher than in New England? Use ? = 0.01. Solve the problem using both the traditional method and the P-value method. (Test the difference ?1 − ?2. Round the test statistic and critical value to three decimal places.) test statistic critical value