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

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.2: Expected Value And Variance Of Continuous Random Variables

Problem 10E

See similar textbooks

Related questions

Q: In a sample of 30 participants, a researcher estimates the 95% CI for a sample with a mean of Μ1-Μ2…

A: From the given questionSample size (n) =30, mean difference (M1-M2) =0.7 and standard error…

Q: Past experience indicates that the time required for high school seniors to complete a standardized…

Q: In a simple random sample of 46 oral temperatures, the mean was 37.3 degrees Celsius with a standard…

A: It is given that n=46, df=45, x=37.3 and s=1.1. The test isH0:μ=37H1:μ>37

Q: A sample of size 10 has a sample mean of 1000 and a sample variance of 100. Then a 90% Confidence…

A: We have given that, Sample mean (x̄) = 1000 and sample variance (s^2) = 100 and sample size (n) =…

Q: In a random sample of 5000 UWC students, 2846 claimed to live in one of the campus’s residences.…

A: Given information- Sample size, n = 5000 We have given that out of 5000 UWC students, 2846 claimed…

Q: 4.) A random sample of 25 students obtained a mean of 78 and a variance of s = 15 on a college…

A: Givensample size(n)=25mean(x)=78variance(s2)=15confidence level(α)=98%

Q: Assume them to be a random sample from a normal population. Perform a hypothesis test at alpha =…

A: Given: n = 10 variance, σ2 = 0.02 α = 0.05

Q: A two-sample t-test will be conducted to investigate whether the mean number of tickets sold for…

Q: Suppose x has a normal distribution with a population standard deviation of 2.2. If a random sample…

Q: A sample of n = 25 scores is determined to have a standard error of 2 points. what is the standard…

A: Given data, SE=2 n=25 s=?

Q: If the probability of a defective bolt is 0.1, find (a) the mean, and (b) the standard deviation of…

A: here p= probability of defective bolt = 0.1 q = 1-p = 0.9 n= 900 here use binomial theorem because…

Q: A sample of n = 4 scores is selected from a population with an unknown mean. The sample has a mean…

A: This simple confidence interval uses a t statistic and sample mean (M) to generate an interval…

Q: f a random sample of size n = 20 from a normal population with the variance = 25 has the mean ī =…

Q: For a two-tailed test at 86.12% confidence, if is known the critical value is

A: It is given that, the confidence level is 86.12.

Q: The sugar content of the syrup in canned peaches is normally distributed, and the variance is…

A: Givensample size(n)=10standard deviation(s)=4confidence interval = 95%

Q: A sample of n = 16 scores has a mean of M = 58 with SS = 960. Use the sample to construct the 90%…

A: Given N = 16 M = 58 SS = 960 C1 = 90 For SS we will solve S2 = 64 df = n-1 = 16-1 =15

Q: A sample with a variance of s2 = 36 has a standard deviation equal to s = 6. Tru or false

Q: To test whether or not there is a significant difference in the average snowfall in Maryland, and…

A: The provided sample means are shown below: Xˉ1=5.4\bar X_1 = 5.4 Xˉ2=5.2\bar X_2 = 5.2 Also, the…

Q: Assume that the population is normally distributed and that the sample has been randomly selected. A…

A: Solution: From the given information, the sample variance is S=4.7 cm, population variance is σ=3.5…

Q: A sample of n = 25 scores has a mean of x̅ = 65 and an estimated standard error of sx̅ = 2 points.…

A: The standard error is 2 points.

Q: A sample of certain observations selected from a normally distributed population produced a sample…

A: Given that Population produced sample variance=S2 =38 Confidence interval=98%

Q: a sample of n=16 scores has mean of M=58 with SS=540. Use the sample to construct the 95% confidence…

A: Solution: From the given information, n=16, M=58 and SS=540.

Q: suppose the random variable X has a normal distribution with a mean of 10 and a variance of 16…

A: Given information: X is a random variable follows normal distribution. That means,

Q: A random sample of n = 16 scores is obtained from a normal population with a mean of µ = 100 and a…

Q: A researcher found that a cigarette smoker smokes on average 30 cigarettes a day. She feels that…

Q: A sample of 20 cans of tomato juice showed a standard deviation of 0.4 ounces. A 95% confidence…

A: we have given that, sample size = 20 standard deviation = 0.4 now, variance= (standard deviation)^2…

Q: A homeowner estimates that within the range of likely temperatures his January heating bill, Y, in…

A: Given : Y = 290 - 5T Where T is a r.v with Mean (μT) = 24 S.D (σT) = 4

Q: A símple random sample of size 100 has mean 15, the population variance being 25. Find an interval…

Q: Suppose that the lengths, in inches, of adult corn snakes are normally distributed with an unknown…

A: Introduction: The 100 (1 – α) % confidence interval for the population mean, μ, when the population…

Q: A study claims tha.t on average, male high school students spend at least 3.39 hours a day playing…

A: The summary of the statistics is, x¯=4.12,σ=2.05,n=30μ=3.39 The formula for calculating the z-score…

Q: Compute the standard score (Z-score) for x, when x = 42, the mean of the distribution = 26, and the…

A: x = 42Mean = 26Standard deviation = 8

Q: A person read that the average number of hours an adult sleeps on Friday night to Saturday morning…

A: test statistic=t=X¯-μs/nX¯=7.7, s=1.3, n=14, tcritical=tα,n-1= 1.7709 one-tailed test

Q: A sample of size 12 has d mean of 29 and a standard deviation of 6. Assuming the population is…

A: Given that sample size n = 12 Sample mean = 29 Sample SD = 6 The critical value of t at (n - 1) = 11…

Q: Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1. If P(0…

A: We have given that z-scores are normally distributed with a mean of 0 and a standard deviation of 1.

Q: How large a sample is needed for a correlation of r = 0.54 to be significant using a two-tailed test…

A: It is given that the level of significance is 0.05.

Q: A sports psychologist tests a new coaching method and finds that of the 43 novice athletes who were…

Q: A study at the University of Colorado at Boulder shows that running increases the percent resting…

A: The average RMR of 30 elderly women runners was 34.0% higher than the average RMR of 30 sedentary…

Q: A manufacturer of sports equipment has developed a new synthetic fishing line that he claims has a…

Q: The proportion of defective microcomputer disks of a certain kind is believed to be anywhere from…

Q: In a random sample of size 11 from normally distributed population, obtain 99% confidence limits for…

Q: A study was done on body temperatures of men and women. The results are shown in the table. Assume…

A: Statistical Software Output:

Q: f a random sample of 100 vehicles is selected, calculate the standard error of the sample means

A: Concept and formula: The standard error is known as the estimated value of the standard deviation of…

Q: A person read that the average number of hours an adult sleeps on Friday night to Saturday morning…

A: Given Population mean, μ=7.4 Sample Size, n=16 Sample mean, X=6.2 Sample sd, s=1.1 α=0.05

Q: A sample of n = 4 scores is selected from a population with an unknown mean. The sample has a mean…

Q: suppose the random variable X has a normal distribution with a mean of 10 and a variance of 16…

A: Given: The random variable X is normally distributed. The population mean is given as:…

Q: A sample of n = 4 scores has a variance of s2 = 16 and an estimated standard error of 2.

A: Given: Sample size, n=4 Variance, s2 = 16 Compute standard deviation: σ=s2=16=4

Q: random sample of 20 students yielded a mean of = 72 and a variance of s2 = 16 for scores on a…

Q: The recovery time from COVID19 is normally distributed with a mean of 12 days and a standard…

A: The random variable recovery time follows normal distribution. The population mean is 12. The…

Q: A researcher wishes to see if the average number of sick days a worker takes per year is greater…

A: Given , Sample size = n = 32 Sample mean = x¯ = 5.3 Population standard deviation = σ = 1.2 Claim…

Question

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

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Expert Solution