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- Are birthdays "evenly distributed" throughout the year, or are they more common during some parts of the year than others? Owners of a children's toy store chain in the Northwest asked just this question. Some data collected by the chain are summarized in the table below. The data were obtained from a random sample of 190 people. The birthdate of each person was recorded, and each of these dates was placed into one of four categories: winter (December 21-March 20), spring (March 21-June 20), summer (June 21-September 20), and fall (September 21-December 20). The numbers in the first row of the table are the frequencies observed in the sample for these season categories. The numbers in the second row are the expected frequencies under the assumption that birthdays are equally likely during each season of the year. The bottom row of numbers gives the following value for each of the season categories. Answer the following to summarize the test of the hypothesis that birthdays are equally…Among drivers who have had a car crash in the last year, 110 were randomly selected and categorized by age, with the results listed in the table below. Age Under 25 25-44 45-64 Over 64 Drivers 44 24 15 27 If all ages have the same crash rate, we would expect (because of the age distribution of licensed drivers) the given categories to have 16%, 44%, 27%, 13% of the subjects, respectively. At the 0.05 significance level, test the claim that the distribution of crashes conforms to the distribution of ages. The test statistic is x²= The critical value is x² = The conclusion is OA. There is sufficient evidence to warrant the rejection of the claim that the distribution of crashes conforms to the distibuion of ages. OB. There is not sufficient evidence to warrant the rejection of the claim that the distribution of crashes conforms to the distibuion of ages.A random sample of 10 compact cars, 10 mid-size cars, and 10 luxury cars were selected. The time (in seconds) each of the randomly selected cars required to accelerate from 0 to 60 mph was looked up on the Autos.com website. The results are presented below. Car Type Time (in seconds) Required to Accelerate from 0 to 60 mph Compact 9.3 8.1 10.2 8.8 9.0 9.3 7.7 9.2 9.4 8.6 Mid-Size 6.9 5.7 8.3 7.7 8.6 5.9 6.1 8.8 6.1 7.2 Luxury 5.7 6.3 5.4 4.7 6.2 7.0 5.9 5.3 6.3 5.0 Conduct a hypothesis test using ! = 0.05 to determine whether the mean time required to accelerate from 0 to 60 mph is the same for compact, mid-size, and luxury cars. (No accounting or excel, I need help solving it.)
- A random sample of eight pairs of twins was randomly assigned to treatment A or treatment B. The data are given in the following table.Twins : 1 2 3 4 5 6 7 8Treatment A: 48.3 44.6 49.7 40.5 54.3 55.6 45.8 35.4Treatment B: 43.5 43.8 53.7 43.9 54.4 54.7 45.2 34.4a. Is there significant evidence that the two treatments differ using an α = 0.05 paired t test.b. Place a 95% confidence interval on the mean difference between the responses from the two treatments.The types of browse favored by deer are shown in the following table. Using binoculars, volunteers observed the feeding habits of a random sample of 320 deer. Type of Browse Plant Compositionin Study Area Observed Number of DeerFeeding on This Plant Sage brush 32% 103 Rabbit brush 38.7% 134 Salt brush 12% 38 Service berry 9.3% 23 Other 8% 22 Use a 5% level of significance to test the claim that the natural distribution of browse fits the deer feeding pattern. State the null and alternate hypotheses. A) 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.) B) Estimate the P-value of the sample test statistic. C) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis that the…A real-estate appraiser wants to verify the market value for homes on the east side of the city that are very similar to size and style. The appraiser wants to test the popular belief that the average sales price is $37.80 per square foot for such homes. Suppose that a random sample of six sales were selected. The sampled sales prices per square foot are $35.00, $38.10, $37.20, $29.80, $30.30, and $35.40. Assuming a normal distribution is a good model for sales, test the claim that the mean sales price per square foot differs from $37.80 at the 1% significance level.
- 46% of all statistics classes require an advanced calculator and 38% require the use of a computer that has statistical software. Of the classes that require an advanced calculator, 18% also require the use of a computer. If a statistics course is selected at random find A. P(Advanced Calculator) = [ Select ] ["0.57", "0.38", "0.18", "0.46"] B. P(Statistical Software) = [ Select ] ["0.38", "0.57", "0.46", "0.18"] C. P(Require an Advanced Calculator and Statistical Software) = [ Select ] ["0.1259", "0.1748", "0.0828", "0.8335"] D. P(Require an Advanced Calculator GIVEN Require Statistical Software) = [ Select ] ["0.3515", "0.18", "0.2184", "0.9716"]Myers-Briggs: Personality Types Isabel Briggs Myers was a pioneer in the study of personality types. The personality types are broadly defined according to four main preferences. Do married couples choose similar or different personality types in their mates? The following data give an indication (Source: I.B. Myers and M.H. Mccauley, A Guide to the Development and Use of tile Myers-Briggs Type Indicators). Similarities and Differences in a Random Sample of 375 Married Couples Number of Similar Preferences Number of Married Couples All four 34 Three 131 'I\vo 124 One 71 None 15 Suppose that a married couple is selected at random. Use the data to estimate the probability that they will have 0, 1, 2, 3, or 4 personality preferences in common. So the probabilities add up to 1? Why should they? V\lnat is the sample space in this problem?A random survey of health issues, conducted by the Department of Public Health of the Commonwealth of Massachusetts, examined the results from the state's seven largest cities. These cities were selected on the basis of their diverse racial and ethnic populations. The percentage of adults with diabetes in each city in the survey is given in the following table. City Boston Worcester Springfield Lowell Fall River Lawrence NewBedford Adults withDiabetes (%) 4.2 5.2 9.1 5.7 8.1 7.9 6.3 Find the average percentage of adults with diabetes in these seven cities. (Round your answer to two decimal places.) %What is the standard deviation for these data? (Round your answer to two decimal places.) %
- Two pieces of information were gathered from 1212 randomly selected cities in the United States: the number of persons owning registered firearms and the murder rate. It was observed that cities with more registered firearms tended to have higher murder rates. Part A: Which is the population of interest in this study? People who own registered firearms in the United States Cities in the United States People who live in U.S. cities People who were murdered in the United States Part B: Which is the sample in this study? People who live in the 121U.S. cities People who own registered firearms in the 12 U.S. cities 12 cities in the United States People who were murdered in the 12 U.S. cities Part C: What type of study is this? A census, because it uses data from the entire population A statistical study, because it uses data from a sample Part D: Which of the following was not a variable observed in this study? The number of registered firearms in a given city Murder…Consider the following two sets of history class final test scores: X: 88, 15, 22, 93, 72 Y: 50, 52, 59, 61, 56 A. Which of these sets of scores was more likely drawn from a sample with the greater Variance? B. Why?This year’s water pollution readings at State Park Beach seem to be lower than last year. A sample of 30 readings was randomly selected from this year’s daily readings: 3.6 3.9 3.3 3.4 3.8 3.7 3.5 3.6 3.7 3.6 3.6 3.7 3.9 3.8 3.7 4.0 3.7 3.5 3.8 3.6 3.5 3.6 3.5 3.7 3.6 3.9 3.9 3.7 3.6 3.5 Researchers want to know if this is sufficient evidence to conclude that the mean of this year’s pollution readings is significantly lower than last year’s mean of 3.8. If the p-value is less than 0.0001, what is your decision (let α = 0.05) ? Retain Ho Reject Ho
