Construct a 95% confidence interval for σ2
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A: Answer Sample size [n] =28Standard deviation =1.7Variance [1.7]^2 =2.89
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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 σ2 . Assume the population of battery
lives to be approximately
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- Researchers interested in determining the relative effectiveness of two different drug treatments on people with a chronic illness established two independent test groups. The first group consisted of 14 people with the illness, and the second group consisted of 12 people with the illness. The first group received treatment 1 and had a mean time until remission of 172 days with a standard deviation of 8 days. The second group received treatment 2 and had a mean time until remission of 183 days with a standard deviation of 5 days. Assume that the populations of times until remission for each of the two treatments are normally distributed with equal variance. Construct a 95% confidence interval for the difference u, -H, between the mean number of days before remission after treatment 1 (u,) and the mean number of days before remission after treatment 2 (u). Then find the lower limit and upper limit of the 95% confidence interval. Carry your intermediate computations to at least three…Don't use the function key on the calculator, or any other technology to find the probabilities, and use Standard Normal Table. A study was conducted to determine whether or not magnets were effective in treating lower back pain. The control group was given a sham treatment ( similar to a placebo. Pain was measured using the visual analog scale. Reduction in pain level for the 100 patients given the magnet treatment was an average of 0.49, and a standard deviation of 0.96. Reduction in pain level for the 100 patients given the sham treatment was an average of 0.44, and a standard deviation of 1.4. Test at the 95% confidence level to determine whether or not the magnet therapy was effective. Use a two tailed test of hypothesis. Use the p-value method to form your conclusion. Clearly show what two values you are comparing to make your decision.Some manufacturers claim that non-hybrid sedan cars have a lower mean miles-per-gallon (mpg) than hybrid ones. Suppose that consumers test 254 hybrid sedans and get a mean of 26 mpg with a standard deviation of 4 mpg. Also, 237 non-hybrid sedans get a mean of 24 mpg with a standard deviation of 6 mpg. Suppose that both populations are known to be normal distributed. Conduct a hypothesis test to evaluate the manufacturers' claim. Test at a 4% level of significance. Let population 1 denote non-hybrids and population 2 denote hybrids. (a) H0 : μ1 ______ μ2 (b) Ha : μ1 _______ μ2 (c) In words, state what your random variable represents.The random variable is the (mean / difference in the / difference in the mean) miles per gallon of non-hybrid sedans and hybrid sedans.
- A psychologist wants to test whether there is any difference in puzzle-solving abilities between boys and girls. Independent samples of eleven boys and seven girls were chosen at random. The boys took a mean of 37 minutes to solve a certain puzzle, with a standard deviation of 4.8 minutes. The girls took a mean of 35 minutes to solve the same puzzle, with a standard deviation of 4.5 minutes. Assume that the two populations of completion times are normally distributed, and that the population variances are equal. Can we conclude, at the 0.10 level of significance, that the mean puzzle-solving times for boys, μ1 is greater than the mean puzzle-solving times for girls, μ2? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. a. State the null hypothesis H0 and the alternative hypothesis H1. b. Find the value of the test statistic. (Round to three or more decimal…Pilots who cannot maintain regular sleep hours due to their work schedule often suffer from insomnia. A recent study on sleeping patterns of pilots focused on quantifying deviations from regular sleep hours. A random sample of 28 commercial airline pilots was interviewed, and the pilots in the sample reported the time at which they went to sleep on their most recent working day. The study gave the sample mean and standard deviation of the times reported by pilots, with these times measured in hours after midnight. (Thus, if the pilot reported going to sleep at p.m., the measurement was -1.) The sample mean was 0.8 hours, and the standard deviation was 1.6 hours. Assume that the sample is drawn from a normally distributed population. Find a 90% confidence interval for the population standard deviation, that is, the standard deviation of the time (hours after midnight) at which pilots go to sleep on their work days. Then give its lower limit and upper limit.A sample of 14 male college students consumes an average of 14.3 gallons of beer per month, with a sample standard deviation of 5.2 gallons. You can safely assume that the population of monthly beer consumption is Normally distributed. What is the margin of error for a 90% Confidence Interval for the mean? (Leave your answer to two decimal places, ex: 18.12)
- do number (d), (e), and (f) pleaseSuppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 24 days and a standard deviation of 6 days. 80% of all trials of this type are completed within how many days?A researcher decides to measure anxiety in group of bullies and a group of bystanders using a 23-item, 3 point anxiety scale. Assume scores on the anxiety scales are normally distributed and the variance among the group of bullies and bystanders are the same. A group of 30 bullies scores an average of 21.5 with a sample standard deviation of 10 on the anxiety scale. A group of 27 bystanders scored an average of 25.8 with a sample standard deviation of 8 on the anxiety scale. You do not have any presupposed assumptions whether bullies or bystanders will be more anxious so you formulate the null and alternative hypothesis based on that.
