stat quiz 8a

A Labrador retriever club has 130 members: 65 black Labs, 44 golden Labs, and 21 chocolate Labs. Pablo is going to perform a chi-square goodness-of-fit test to see if the distribution of Labrador retrievers in the club is the same as the distribution nationally. Pablo is going to test his sample against the following null hypothesis, which reflects the national distribution. H0:pblack=0.53,pgolden=0.39,pchocolate=0.08 If the distribution of Labrador retrievers in the club were to match that of the national average, how many of each type of Labrador retriever would Pablo expect to see in his club? A 68.9, 50.7, 10.4 B 50, 33.8, 16.2 C 65, 44, 21 D 43.3, 43.3, 43.3 E 69, 51, 10

A. 68.9, 50.7, 10.4

A χ2 goodness-of-fit test where all assumptions were met yielded the chi-square test statistic χ2=1.92 and a corresponding p-value of 0.75. The researcher interpreted the p-value as a 0.75 probability of observing a test statistic of χ2=1.92 or larger. What is wrong with the researcher's interpretation? A The researcher did not state that the p-value is conditional on the null hypothesis being true. B The researcher interpreted the p-value as the probability of observing 1.92 exactly. C The alternative hypothesis is not stated. D The significance level is not stated. E The degrees of freedom are not stated.

A. The researcher did not state that the p-value is conditional on the null hypothesis being true.

A job candidate at a large job fair can be classified as unacceptable, provisional, or acceptable. Based on past experience, a high-quality candidate is expected to get 80 percent acceptable ratings, 15 percent provisional ratings, and 5 percent unacceptable ratings. A high-quality candidate was evaluated by 100 companies and received 60 acceptable, 25 provisional, and 15 unacceptable ratings. A chi-square goodness-of-fit-test was conducted to investigate whether the evaluation of the candidate is consistent with past experience. What is the value of the chi-square test statistic and number of degrees of freedom for the test? A χ2=(15−5)^2/5+(25−15)^2/15+(60−80)^2/80 with 2df B χ2=(15−5)^2/5+(25−15)^2/15+(60−80)^2/80 with 3df C χ2=(15−5)^2/5+(25−15)^2/15+(60−80)^2/80 with 99df99df D χ2=(5−15)^2/15+(15−25)^2/25+(80−60)^2/60 with 2df2df E χ2=(5−15)^2/15+(15−25)^2/25+(80−60)^2/60 with 3df

A. χ2=(15−5)^2/5+(25−15)^2/15+(60−80)^2/80 with 2df

A recent article published in Berry Weekly reported a probability distribution for the different types of jelly that individuals prefer. Editors from a competitive magazine, Jammin, conducted their own study to test the distribution. The editors from Jammin surveyed a random sample of 50 individuals and recorded the observed counts of individuals for each jelly type. They decided to test Berry Weekly's claim using a chi-square goodness-of-fit test using Jammin's observed counts compared with the number of expected counts based on the Berry Weekly data. Which of the following is the correct null hypothesis for the test? A H0:pS=0.165 , pG=0.11, pWB=0.095, pp=0.075, pO=0.055 B H0:pS=0.33,pG=0.22,pWB=0.19,pp=0.15,pO=0.11 C H0:H0: At least one of the proportions is different. D H0:pS=0.18,pG=0.12,pWB=0.08,pp=0.06,pO=0.06 E H0:pS=0.36,pG=0.24,pWB=0.16,pp=0.12,pO=0.12

B. H0:pS=0.33,pG=0.22,pWB=0.19,pp=0.15,pO=0.11

A sports fan conducted a test to investigate whether male high school athletes are equally divided among football, soccer, swimming, tennis, and basketball. A sample of male high school athletes was selected and the resulting value of the chi-square test statistic was 10.65. Which of the following represents the p-value? A P(χ2≥10.65)=0.00 B P(χ2≥10.65)=0.03 C P(χ2≥10.65)=0.06 D P(χ2≥10.65)=0.94 E P(χ2≥10.65)=0.97

B. P(χ2≥10.65)=0.03

Which of the following best describes the shape of the chi-square distribution when the degrees of freedom are less than 10 ? A Unimodal and symmetric B Skewed to the right C Skewed to the left D Uniform E Bimodal

B. Skewed to the right

Which of the following describes a scenario in which a chi-square goodness-of-fit test would be an appropriate procedure to justify the claim? A A statistician would like to show that one geographical location has a higher proportion of dogs that shed than another geographical location has. The statistician has two independent random samples of dogs from two different geographical locations and has recorded the proportion of dogs that shed in each sample. B A principal would like to investigate whether more than 50% of the students in a local high school eat in the school cafeteria. The principal has a random sample of individuals within the school and records the proportion of the students who eat lunch in the school cafeteria. C A campaign manager would like to show that the distribution of individuals within several social economic categories is different than what a newspaper reported. The campaign manager has a random sample of potential voters in a large city and records the number of individuals within each of the categories. D A manager of a water treatment plant would like to investigate whether there is a relationship between the amount of chemical used and the number of bacteria present in the water treated at the plant. The manager measures the level of bacteria from tanks at the facility that each received a different level of chemical treatment. E City officials would like to estimate the average price of gas in their city. The officials have a random sample of gas prices at several gas stations within their city limits.

C. A campaign manager would like to show that the distribution of individuals within several social economic categories is different than what a newspaper reported. The campaign manager has a random sample of potential voters in a large city and records the number of individuals within each of the categories.

A major credit card company is investigating whether the distribution of the number of credit cards used by its customers has changed from last year to this year. Customers are classified as using 1 card, 2 cards, or more than 2 cards. The company conducts a chi-square goodness-of-fit test to investigate whether there is a change in the distribution of number of cards used from last year to this year. The value of the chi-square test statistic was χ2=7.82 with a corresponding p-value of 0.02. Assuming the conditions for inference were met, which of the following is the correct interpretation of this p-value? A There is a 2 percent chance that the company's claim is correct. B There is a 2 percent chance of obtaining a chi-square value of at least 7.82. C If the null hypothesis were true, there is a 2 percent chance of obtaining a chi-square value of at least 7.82. D If the null hypothesis were true, there is a 2 percent chance that the company's claim is correct. E If the null hypothesis were true, there is a 2 percent chance of obtaining a chi-square value of 7.82.

C. If the null hypothesis were true, there is a 2 percent chance of obtaining a chi-square value of at least 7.82.

A researcher is investigating the claim that the proportion of television viewers who identify one of four shows as their favorite is the same for all four shows. A χ2 goodness-of-fit test at a significance level of α=0.05 produced the test statistic χ2=8.95 with a corresponding p-value of 0.03. Which of the following is correct? A There is sufficient evidence to reject the null hypothesis at the 0.05 level since the test statistic is greater than the p-value. B There is not sufficient evidence to reject the null hypothesis at the 0.05 level since the test statistic is greater than the p-value. C There is sufficient evidence to reject the null hypothesis at the 0.05 level since the p-value is less than the significance level. D There is not sufficient evidence to reject the null hypothesis at the 0.05 level since the p-value is less than the significance level. E There is sufficient evidence to reject the null hypothesis at the 0.05 level since the test statistic is greater than the significance level.

C. There is sufficient evidence to reject the null hypothesis at the 0.05 level since the p-value is less than the significance level.

A round spinner is divided into five sections, where the sections do not have the same size. Using the measure of the interior angles, the probability of the spinner landing on any individual space on a spin is calculated and given in the table. A statistics student is asked to test the integrity of the spinner using a chi-square goodness-of-fit test. What is the minimum number of times the spinner should be spun to conduct this test? A 5 B 25 C 50 D 100 E 500

D. 100

The table displays the distribution of the percentage of different types of home heating sources for a large mountain city, as reported by the city newspaper. A chi-square goodness-of-fit test will be performed using a simple random sample of 100 homes to investigate whether the proportion of homes heated with each source is the same as what is reported by the newspaper. Which of the following represents the alternative hypothesis of the test? A The proportions for the different heating systems match those reported by the newspaper. B At least one of the heating source proportions is the same as the corresponding proportion reported by the newspaper. C The heating sources are not evenly distributed between homes. D At least one of the heating source proportions is different from the proportion reported by the newspaper. E Wood stove heating represents the highest proportion of heating source.

D. At least one of the heating source proportions is different from the proportion reported by the newspaper.

A national publication showed the following distribution of favorite class subjects for high school students. Pasquale, a student from a high school of 1,200 students, wants to see whether the distribution at his school matches that of the publication. He stands at the school entrance in the morning and asks the first 40 students he sees what their favorite class is. Pasquale records the following table of observed values. He decides to conduct a chi-square goodness-of-fit test to see whether his high school's distribution differs significantly from that of the publication. Pasquale's statistics teacher tells him that his information does not meet the conditions necessary for a goodness-of-fit test. Which condition has not been met? Data are collected using a random sample or randomized experiment n≤0.10N All expected counts are greater than 5. A II only B IIII only C IIIIII only D II and IIIIII only E II and IIII only

D. I and III only

A chi-square goodness-of-fit test using a significance level of α=0.05 was conducted to investigate whether the number of babies born in a town is uniformly distributed across the months of the year. The test produced a test statistic of χ2=5.6 with a corresponding p-value of 0.90. Which of the following is correct? A Births are uniformly distributed across months. B There is sufficient evidence to suggest that the distribution of births is not uniformly distributed across months. C There is sufficient evidence to suggest that the distribution of births is uniformly distributed across months. D There is insufficient evidence to suggest that the distribution of births is not uniformly distributed across months. E There is insufficient evidence to suggest that the distribution of births is uniformly distributed across months.

D. There is insufficient evidence to suggest that the distribution of births is not uniformly distributed across months.

Jana, a high school principal, hosted a movie event at her school. Jana's assistant kept track of the number of students in each grade who attended the event. The distribution shown in the table represents the number of students in each grade that were present. Jana knows that the grade levels are equally distributed across the school of 1,200 students. She would like to use a chi-square test to see if the proportion of individuals in each class at the movie are also equally distributed. How many seniors would be expected at the event? A 840 B 352.9 C 300 D 70 E 59.5

E. 59.5

An amusement park keeps track of the percentage of individuals with season passes according to age category. An independent tourist company would like to show that this distribution of age category for individuals buying season passes is different from what the amusement park claims. The tourist company randomly sampled 200 individuals entering the park with a season pass and recorded the number of individuals within each age category. The tourist company will use the data to test the amusement park's claim, which is reflected in the following null hypothesis. H0:pchild=0.23, pteen=0.45, padult=0.20, and psenior=0.12. What inference procedure will the company use to investigate whether or not the distribution of age category for individuals with season passes is different from what the amusement park claims? A A one-sample z-test for a population proportion B A two-sample z-test for a difference between population proportions C A matched pairs t-test for a mean difference D A chi-square test for homogeneity E A chi-square goodness-of-fit test

E. A chi-square goodness-of-fit test

A bag of candy contains 5 different types of colored candies; red, green, blue, yellow, and orange. According to the manufacturer, bags should contain an equal number of each color. Students in a statistics class decided to use a chi-square procedure to test the manufacturer's claim. They opened a bag of candy and recorded the number of candies of each color. The results are shown in the following table. Which color contributes most to the chi-square test statistic? A Red B Green C Blue D Yellow E Orange

E. Orange