A random sample of 25 students obtained a mean of 78 and a variance of s2 = 15 on a college entrance exam in engineering. Assuming the scores are normally distributed, construct a 98% confidence interval of σ2

A random sample of 25 students obtained a mean of 78 and a variance of s2 = 15 on a college entrance exam in engineering. Assuming the scores are normally distributed, construct a 98% confidence interval of σ2

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

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…
If 10 measurements of the density of a certain kind of glass had a variance of 0.0012, construct a 95% confidence interval for σ2, which measures the true variability of the density of this kind of glass.
The time necessary to complete the technical interview for the Google intership is normally distributed with a mean of sixty-three minutes, and a standard deviation of twelve minutes. Let the random variable X represent the number of minutes a randomly chosen student takes to complete the assessment. If a sample of three dozen students is taken, what is the standard deviation of the sample mean σX¯ and what is the probability that the sample mean would be 59 minutes or fewer?
Data provided by the National Association of College Employers indicated that the average starting salary for graduates with a Bachelors Degree in Accounting was $37,000 in 2008. In June 2010 a sample of 48 graduating accounting majors provided a sample average starting salary of $38,100, with a sample standard deviation of $5200. Conduct a hypothesis test to determine if it can be assumed that accounting graduates in 2010 had higher average salaries than graduates in 2008, using α = .05.
A manufacturer claims that the mean lifetime, u, of its light bulbs is 44 months. The standard deviation of these lifetimes is 7 months. Twenty-three bulbs are selected at random, and their mean lifetime is found to be 48 months. Assume that the population is normally distributed. Can we conclude, at the 0.01 level of significance, that the mean lifetime of light bulbs made by this manufacturer differs from 44 months? Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H,. p H, :0 H, :0 (b) Determine the type of test statistic to use. (Choose one) v O=0 OSO |(c) Find the value of the test statistic. (Round to three or more decimal places.) O
A random sample of 23 bags of apples (marked as 10 pounds each) received by a large grocery chain tested out as having a mean of 9.2 pounds with a variance of 2.56 pounds. Test whether the true mean of all bags is under 10 pounds. Set up hypotheses. Perform the appropriate test by showing your formula. Interpret the results using a Type I (alpha) error of .05. Also provide the p value here. Also construct a 95% confidence interval around your sample mean (X bar) that should contain the true mean (mu). Also interpret this interval.
A manufacturer claims that the mean lifetime, u, of its light bulbs is 42 months. The standard deviation of these lifetimes is 6 months. Twenty-seven bulbs are selected at random, and their mean lifetime is found to be 41 months. Assume that the population is normally distributed. Can we conclude, at the 0.01 level of significance, that the mean lifetime of light bulbs made by this manufacturer differs from 42 months? Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H1. p H, :0 H, :0 (b) Determine the type of test statistic to use. D=D OSO (Choose one) (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the two critical values. (Round to three or more decimal places.) Dand (e) Can we conclude that the mean lifetime of…
A study was conducted to compare to brands of milk. Random sample A of 25 packs of milk with a mean content of 237 grams and standard deviation of 8.56 grams. Another sample B of 20 packs of milk showed a mean content of 240 grams and standard deviation of 9.75 grams. Using 0.05 level of significance will we agree that sample A exceeds that of sample B by 2 grams nutrient content, conduct hypothesis testing assuming that variances are equal.
A carpenter is making doors that are 2058 millimeters tall. If the doors are too long they must be trimmed, and if they are too short they cannot be used. A sample of 61 doors is made, and it is found that they have a mean of 2044 millimeters with a variance of 729. Is there evidence at the 0.05 level that the doors are either too long or too short? State the null and alternative hypotheses for the above scenario.
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.
A research tea believes that the weight of Grizzly adule male bears are normally distributed. A simple random saple of 23 Grizzly male bears yielded a mean weight of 277kg and a variance of 121. Let μ denote the mean weight for Grizzly adult male bears. Suppose the research teams wants to test, at the 5 % level of significance, whether the mean weight for Grizzly adult male bears is greater than 271kg. Suppose the assumptions to this hypothesis test are satisifed. a) What are the null and alternative hypothesis, and level of significance, for this hypothesis test? b) What is the distribution of the test statistic for this hypothesis test? c)What is the decision rule for this hypthesis test?
A researcher makes a research about the life time of batteries which have a normal distribution with mean of 50 hours and variance of 9 hours. In order to understand the life time of batteries s/he randomly selected 9 batteries and calculate the sample mean as 48 hours and standard deviation of 5 hours. Construct 80 % confidence interval for the true population mean of life time of batteries. 1- a) (45.43, 50.57) b) (46.04, 49.96) c)O There is no correct answer d) (46.72, 49.28) e) (46.36, 49.65) Boş bırak