The following table shows the Myers-Briggs personality preferences for a random sample of 406 people in the listed professions. E refers to extroverted and I refers to introverted.   Personality Type   Occupation E I Row Total Clergy (all denominations) 61 46 107 M.D. 71 91 162 Lawyer 54 83 137 Column Total 186 220 406 Use the chi-square test to determine if the listed occupations and personality preferences are independent at the 0.05 level of significance. (a) What is the level of significance?   (b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)   What are the degrees of freedom? (c) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.)

An article about the California lottery gave the following information on the age distribution of adults in California: 35% are between 18 and 34 years old, 51% are between 35 and 64 years old, and 14% are 65 years old or older. The article also gave information on the age distribution of those who purchase lottery tickets. The following table is consistent with the values given in the article. Suppose that the data resulted from a random sample of 200 lottery ticket purchasers. Based on these sample data, is it reasonable to conclude that one or more of these three age groups buys a disproportionate share of lottery tickets? Use a chi-square goodness-of-fit test with ? = 0.05. Age of Purchaser Frequency 18–34 36 35–64 130 65 and over 34 Calculate the test statistic. (Round your answer to two decimal places.) ?2 =  Use technology to calculate the P-value. (Round your answer to four decimal places.) P-value =  What can you conclude? The data     strong evidence to conclude…

The following table is from a publication. The individuals in the following table have an eye irritation, a nose irritation, or a throat irritation. They have only one of the three. Is there sufficient evidence to reject the hypothesis that the type of ear, nose, or throat irritation is independent of the age group at a level of significance equal to 0.05?   Age (years) Type of Irritation         18-29     30-44     45-64     65 and Older Eye 422 560 340   54 Nose 932 1324 802 101 Throat 247 309 142  24 (a) Find the test statistic. (Round your answer to two decimal places.)(ii) Find the p-value. (Round your answer to four decimal places.)(b) State the appropriate conclusion. Reject the null hypothesis. There is not significant evidence that this sample contradicts the claim of independence.Reject the null hypothesis. There is significant evidence that this sample contradicts the claim of independence.    Fail to reject the null hypothesis. There is not significant…

A case-control (or retrospective) study was conducted to investigate a relationship between the colors of helmets worn by motorcycle drivers and whether they are injured or killed in a crash. Results are given in the accompanying table. Using a 0.01 significance level, test the claim that injuries are independent of helmet color. D Black Color of Helmet Yellow 32 Blue White 331 Controls (not injured) Red 159 482 100 Cases (injured or 211 109 8 65 47 killed) Click here to view the chi-square distribution table. Identify the null and alternative hypotheses. Choose the correct answer below. O A. Ho: Whether a crash occurs and helmet color are dependent H₁: Whether a crash occurs and helmet color are independent OB. Ho: Injuries and helmet color are dependent H₁: Injuries and helmet color are independent OC. Ho: Whether a crash occurs and helmet color are independent H₁: Whether a crash occurs and helmet color are dependent O D. Ho: Injuries and helmet color are independent H₁: Injuries…

The following table shows a sample dataset of observation values of an independent variable, Age, and a dependent variable, number of toys Age 5 3 6 3 4 4 6 8 Toys 13 15 7 12 13 11 9 5 What is the value of Toys when Age is 7 (round your answer without decimal)

Mitchell works in the produce section at a small local supermarket and would like to test whether the proportion of apples people purchase is the same for each season, using a significance level of 0.05. He analyzes the apple purchases each season for a year and records his findings in the following table. Season Spring Summer Fall Winter Total --------- --------- ------ ------ ------- # of apples purchased 896 934 934 971 3735 (a) In performing this statistical test, state the hypotheses. O Ho: the proportion of customers is the same each season vs. HA: the proportion of customers is not the same each season O Họ: the distribution of apples people purchased is not the same for each season vs. HẠ: the distribution of apples people purchased is the same for each season O Họ: the observed number of apples people purchased is the same for each season vs. Ha: the observed number of apples people purchased is not the same for each season O Họ; the distribution of apples people purchased is…

A survey described the results of a poll of working adults in Canada. Each person in a random sample was classified according to gender and the number of vacation days he or she usually took each year. The resulting data are summarized in the given table. Days of Vacation Gender Male Female None 51 42 1-5 21 25 6-10 67 79 11-15 106 98 16-20 71 70 21-25 82 58 More than 25 118 79 (a) Is it reasonable to conclude that there is an association between gender and the number of vacation days taken?Test the appropriate hypotheses using a 0.05 significance level. Calculate the test statistic. (Round your answer to two decimal places.)?2 =

The type of household for the U.S. population and for a random sample of 411 households from a community in Montana are shown below. Observed Number of Households in the Community Percent of U.S. Type of Household Households Married with children 26% 110 Married, no children Single parent One person Other (e.g., roommates, siblings) 29% 101 32 25% 98 11% 70 Use a 5% level of significance to test the claim that the distribution of U.S. households fits the Dove Creek distribution. (a) What is the level of significance? State the nul and alternate hypotheses. O Ho: The distributions are different. H: The distributions are the same. O Hg: The distributions are the same. H: The distributions are different. O Hg: The distributions are the same. H: The distributions are the same. O Hg: The distributions are different. H: The distributions are different. (b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to two decimal places. Round the test…

Personality preferences for a random sample of 519 people in the listed professions are shown in the following table. T refers to THINKING and F refers to FEELING. Use the chi-square test to determine if the listed occupations and personality preferences are independent at the 0.01 level of significance.   Occupation T F Row Total Clergy 57 91 148 M.D. 77 82 159 Lawyer 118 94 212 Column Total 252 267 519

Hotel Managers' Personalities. Successful hotel managers must have personality characteristics often thought of as feminine (such as "compassionate") as well as those often thought of as masculine (such as "forceful"). The Bern Sex-Role Inventory (BSRI) is a personality test that gives separate ratings for female and male stereotypes, both on a scale of 1 to 7. A sample of 148 male general managers of three-star and four-star hotels had mean BSRI femininity score y = 5.29 The mean score for the general male population is μ = 5.19. Do hotel managers, on the average, differ significantly in femininity score from men in general? Assume that the standard deviation of scores in the population of all male hotel managers is the same as the σ = 0.78 for the adult male population. (a) State null and alternative hypotheses in terms of the mean femininity score μ for male hotel managers. (b) Find the z test statistic. (c) What is the P-value for your z? What do you conclude about male hotel…