Question

A.) Let x = age in years of a rural Quebec woman at the time of her first marriage. In the year 1941, the population variance of x was approximately ?² = 5.1. Suppose a recent study of age at first marriage for a random sample of 41 women in rural Quebec gave a sample variance s² = 3.0. Use a 5% level of significance to test the claim that the current variance is less than 5.1. Find a 90% confidence interval for the population variance.

What is the level of significance?

Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.)

What are the degrees of freedom?

Find the requested confidence interval for the population variance. (Round your answers to two decimal places.)

lower limit =

upper limit =

B.) The fan blades on commercial jet engines must be replaced when wear on these parts indicates too much variability to pass inspection. If a single fan blade broke during operation, it could severely endanger a flight. A large engine contains thousands of fan blades, and safety regulations require that variability measurements on the population of all blades not exceed ?² = 0.18 mm². An engine inspector took a random sample of 81 fan blades from an engine. She measured each blade and found a sample variance of 0.32 mm². Using a 0.01 level of significance, is the inspector justified in claiming that all the engine fan blades must be replaced?

What is the level of significance?

Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.)

What are the degrees of freedom?

Find a 90% confidence interval for the population standard deviation. (Round your answers to two decimal places.)

lower limit            mm

upper limit           mm

C.) Jim Mead is a veterinarian who visits a Vermont farm to examine prize bulls. In order to examine a bull, Jim first gives the animal a tranquilizer shot. The effect of the shot is supposed to last an average of 65 minutes, and it usually does. However, Jim sometimes gets chased out of the pasture by a bull that recovers too soon, and other times he becomes worried about prize bulls that take too long to recover. By reading journals, Jim has found that the tranquilizer should have a mean duration time of 65 minutes, with a standard deviation of 15 minutes. A random sample of 7 of Jim's bulls had a mean tranquilized duration time of close to 65 minutes but a standard deviation of 26 minutes. At the 1% level of significance, is Jim justified in the claim that the variance is larger than that stated in his journal? Find a 95% confidence interval for the population standard deviation.

What is the level of significance?

Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.)

What are the degrees of freedom?

Find the requested confidence interval for the population standard deviation. (Round your answers to two decimal place.)

lower limit            mm

upper limit           mm

Answer 1

A)

The level of significance is

Hypotheses are:

Given information:

The chi-square statistic for the sample:

The degrees of freedom is:

df=n-1=40

The p-value using excel function "=1-CHIDIST(23.53,40)" is 0.0177.

Since p-value is lesser than 0.05 so we reject the null hypothesis.

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For 90% confidence interval value critical value of chi sqaure statitics will be

The confidence interval for the population variance is

lower limit= 2.15

upper limit= 4.53