Construct a 95% confidence interval for variance and decide if the manufacturer’s claim that variance=1 is valid. Assume the population of battery lives to be approximately normally distributed.
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A manufacturer of car batteries claims that the batteries will last, on average, 3 years with a variance of 1 year. Six of these batteries have lifetimes, in years, as follows:
1.9, 2.4, 3.0, 3.5, 4.2, 5.1
Construct a 95% confidence interval for variance and decide if the manufacturer’s claim that variance=1 is valid. Assume the population of battery lives to be approximately
Round of to 2-5 decimal places.
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- Find the 95% confidence interval for the variance and standard deviation for the time it takes a state police inspector to check a truck for safety if a sample of 21 trucks has a standard deviation of 5.2 minutes. Assume the variable is normally distributed.The table below lists weights (carats) and prices (dollars) of randomly selected diamonds. Find the (a) explained variation, (b) unexplained variation, and (c) indicated prediction interval. There is sufficient evidence o support a claim of a linear correlation, so it is reasonable to use the regression equation when making predictions. For the prediction interval, use a 95% confidence level with a diamond that weighs 0.8 carats. Weight Price 0.3 $508 a. Find the explained variation. 0.4 $1153 0.5 $1332 Round to the nearest whole number as needed.) . Find the unexplained variation. Round to the nearest whole number as needed.) c. Find the indicated prediction interval.A paint manufacturer wants to introduce a new paint on the market. The following data were obtained for drying time (minutes) when five samples of the paint were tested. 380 290 240 310 300 Assuming that the drying time is normally distributed with a variance of 400, obtain a 99% confidence interval for the true mean drying time.Choose the appropriate statistical test. When computing, be sure to round each answer as indicated. A dentist wonders if depression affects ratings of tooth pain. In the general population, using a scale of 1-10 with higher values indicating more pain, the average pain rating for patients with toothaches is 6.8. A sample of 30 patients that show high levels of depression have an average pain rating of 7.1 (variance 0.8). What should the dentist determine? 1. Calculate the estimated standard error. (round to 3 decimals). [st.error] 2. What is thet-obtained? (round to 3 decimals). 3. What is the t-cv? (exact value) 4. What is your conclusion? Only type "Reject" or Retain"Two coworkers commute from the same building. They are interested in whether or not there is any variation in the time it takes them to drive to work. They each record their times for 20 commutes. The first worker's times have a variance of 12.1. The second worker's times have a variance of 16.9. The first worker thinks that he is more consistent with his commute times and that his commute time is shorter. Test the claim at the 10% level. What is s1 in this problem? What is s2 in this problem?In its 2016 Auto Reliability Survey, Consumer Reports asked subscribers to report their maintenance and repair costs. Most individuals are aware of the fact that the average annual repair cost for an automobile depends on the age of the automobile. A researcher is interested in finding out whether the variance of the annual repair costs also increases with the age of the automobile. A sample of 26 automobiles 4 years old showed a sample standard deviation for annual repair costs of $190 and a sample of 24 automobiles 2 years old showed a sample standard deviation for annual repair costs of $100. a. State the null and alternative versions of the research hypothesis that the variance in annual repair costs is larger for the older automobiles. Let 4 year old automobiles be represented by population 1. 0² Ho o less than or equal to H₁: o greater than b. At a 0.01 level of significance, what is your conclusion? Calculate the value of the test statistic (to 2 décimals). Ⓡ The p-value is less…What percentage of Contra Costa County adults supports a ban on assault-style weapons? Suppose that we survey a random sample of 100 adults living in Contra Costa County and find that 62% support a ban on assault-style weapons. According to a 2015 study by the Pew Research Center, 57% of U.S. adults favor a ban on assault-style weapons. Assuming that the variability in random samples will be the same in Contra Costa County as in the U.S., find the 95% confidence interval to estimate the proportion of CCC adults that favor a ban on assault-style weapons. g. Are we confident that the percentage of Contra Costa County residents that supports a ban is greater than the percentage nationwide as reported by the Pew Research Center? Why or why not?In 2016 its Auto Reliability Survey, Consumer Reports asked subscribers to report their maintenance and repair costs. Most individuals are aware of the fact that the average annual repair cost for an automobile depends on the age of the automobile. A researcher is interested in finding out whether the variance of the annual repair costs also increases with the age of the automobile. A sample of 26 automobiles 4 years old showed a sample standard deviation for annual repair costs of $150 and a sample of 25 automobiles 2 years old showed a sample standard deviation for annual repair costs of 1. a. State the null and alternative versions of the research hypothesis that the variance in annual repair costs is larger for the older automobiles. Let year old automobiles be represented by population . b. At a 0.01 level of significance, what is your conclusion? Calculate the value of the test statistic (to 2 decimals). The -value is . Use Table 4 of Appendix B. that 4 year old…You are testing the claim that having lights on at night increases weight gain (abstract). A sample of 10 mice lived in an environment with bright light on all of the time and 8 mice who lived in an environment with a normal light/dark cycle is given below. Test the claim using a 2% level of significance. Assume the population variances are unequal and that the weight changes are normally distributed. Give answers to 3 decimal places. Data available at StatKey, choose Mice Wgt Gain-2e data set Light (1) 1.71 4.67 4.99 5.33 5.43 6.94 7.15 9.17 10.26 11.67 What are the correct hypotheses? Note this may view better in full screen mode. Select the correct symbols in the order they appear in the problem. Ho: ₁ Test Statistic = Dark (₂) 2.27 2.53 2.83 4 4.21 4.6 5.95 6.52 Ha: ₁ Based on the hypotheses, find the following: p-value = = V Select an answer ✓ Select an answer (Hint: difference in means from H₂) The correct decision is to fail to reject the null hypothesis The correct summary…In its 2016 Auto Reliability Survey, Consumer Reports asked subscribers to report their maintenance and repair costs. Most individuals are aware of the fact that the average annual repair cost for an automobile depends on the age of the automobile. A researcher is interested in finding out whether the variance of the annual repair costs also increases with the age of the automobile. A sample of 26 automobiles 4 years old showed a sample standard deviation for annual repair costs of $210 and a sample of 25 automobiles 2 years old showed a sample standard deviation for annual repair costs of $100. (a) State the null and alternative versions of the research hypothesis that the variance in annual repair costs is larger for the older automobiles. (b) At a 0.01 level of significance, what is your conclusion? Find the value of the test statistic. (c) Find the p-value. (Round your answer to four decimal places.) p-value = (d) State your conclusion: A) Reject H0. We can conclude that…Periodically, customers of a financial services company are asked to evaluate the company's financial consultants and services. Higher ratings on the client satisfaction survey indicate better service, with 7 the maximum service rating. Independent samples of service ratings for two financial consultants are summarized here. Consultant A has 10 years of experience, whereas consultant B has 1 year of experience. Use a = 0.05 and test to see whether the consultant with more experience has the higher population mean service rating. Assume the population variances are unequal. Consultant A Consultant B n1 = 16 n2 10 X1 = 6,81 X2 = 6.25 %3D S1 = 0.68 S2 = 0.75 (a) State the null and alternative hypotheses. O Hoi H1 - H2 = 0 Hai H1- Hz>0 O Ho: H1 - 42 = 0 Hại H1 - H2# 0 O Ho: H1 - H2 > 0 %3D Ha: H1 - H2 = 0 O Ho: H1 - Hz # 0 Hai Hy - Hz = 0 Hoi H1 - H2 = Hai H1- H2 = 0 (b) Compute the value of the test statistic. (Round your answer to three decimal places.) 19.191 (c) What is the p-value?…An HIV clinical trial with 1151 subjects was conducted. We will focus on two variables from this trial: IVDrug and Age. IVDrug is a categorical variable that indicates whether each subject never, previously, or currently uses IV drugs. Age lists the subject's age in year. Thus, we have age for subjects in three treatment groups. Assume that the samples were collected independently and come from a normally distributed population with equal variances. An ANOVA is used to test whether average age in the three IV drug groups is the same. A partially filled-in ANOVA table is listed below. Use a significance level of 0.05. p-value Treatment Error Total df SS MS 76.77 F 7.5586
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