Question

A new kind of typhoid shot is being developed by a medical research team. The old...

A new kind of typhoid shot is being developed by a medical research team. The old typhoid shot was known to protect the population for a mean time of 36 months, with a standard deviation of 3 months. To test the time variability of the new shot, a random sample of 23 people were given the new shot. Regular blood tests showed that the sample standard deviation of protection times was 2.1 months. Using a 0.05 level of significance, test the claim that the new typhoid shot has a smaller variance of protection times.

(a) What is the level of significance?


State the null and alternate hypotheses.

Ho: σ2 = 9; H1: σ2 < 9Ho: σ2 < 9; H1: σ2 = 9    Ho: σ2 = 9; H1: σ2 ≠ 9Ho: σ2 = 9; H1: σ2 > 9


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


What are the degrees of freedom?


What assumptions are you making about the original distribution?

We assume a normal population distribution.We assume a uniform population distribution.    We assume a exponential population distribution.We assume a binomial population distribution.


(c) Find or estimate the P-value of the sample test statistic.

P-value > 0.1000.050 < P-value < 0.100    0.025 < P-value < 0.0500.010 < P-value < 0.0250.005 < P-value < 0.010P-value < 0.005


(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

Since the P-value > α, we fail to reject the null hypothesis.Since the P-value > α, we reject the null hypothesis.    Since the P-value ≤ α, we reject the null hypothesis.Since the P-value ≤ α, we fail to reject the null hypothesis.


(e) Interpret your conclusion in the context of the application.

At the 5% level of significance, there is insufficient evidence to conclude that the new typhoid shot has a smaller variance of protection times.At the 5% level of significance, there is sufficient evidence to conclude that the new typhoid shot has a smaller variance of protection times.    


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

lower limit
upper limit    


Interpret the results in the context of the application.

We are 90% confident that σ lies above this interval.We are 90% confident that σ lies outside this interval.    We are 90% confident that σ lies within this interval.We are 90% confident that σ lies below this interval.

Homework Answers

Answer #1

a) level of significance =0.05

Ho: σ2 = 9; H1: σ2 < 9

b)

value of the chi-square statistic =(23-1)*(2.1/3)2 =10.78

degrees of freedom =23-1=22

We assume a normal population distribution.

c) 0.010 < P-value < 0.025

d)

  Since the P-value ≤ α, we reject the null hypothesis

e)

At the 5% level of significance, there is sufficient evidence to conclude that the new typhoid shot has a smaller variance of protection times.    

f)

lower limit =1.69

upper limit =2.80

  We are 90% confident that σ lies within this interval.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A new kind of typhoid shot is being developed by a medical research team. The old...
A new kind of typhoid shot is being developed by a medical research team. The old typhoid shot was known to protect the population for a mean time of 36 months, with a standard deviation of 3 months. To test the time variability of the new shot, a random sample of 19 people were given the new shot. Regular blood tests showed that the sample standard deviation of protection times was 1.9 months. Using a 0.05 level of significance, test...
A new kind of typhoid shot is being developed by a medical research team. The old...
A new kind of typhoid shot is being developed by a medical research team. The old typhoid shot was known to protect the population for a mean time of 36 months, with a standard deviation of 3 months. To test the time variability of the new shot, a random sample of 23 people were given the new shot. Regular blood tests showed that the sample standard deviation of protection times was 1.7 months. Using a 0.05 level of significance, test...
Let x = age in years of a rural Quebec woman at the time of her...
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 σ2 = 5.1. Suppose a recent study of age at first marriage for a random sample of 31 women in rural Quebec gave a sample variance s2 = 2.5. Use a 5% level of significance to test the claim that the current variance is less than 5.1. Find a 90% confidence...
Let x = age in years of a rural Quebec woman at the time of her...
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 σ2 = 5.1. Suppose a recent study of age at first marriage for a random sample of 51 women in rural Quebec gave a sample variance s2 = 3.4. Use a 5% level of significance to test the claim that the current variance is less than 5.1. Find a 90% confidence...
Let x = age in years of a rural Quebec woman at the time of her...
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 σ2 = 5.1. Suppose a recent study of age at first marriage for a random sample of 51 women in rural Quebec gave a sample variance s2 = 2.8. Use a 5% level of significance to test the claim that the current variance is less than 5.1. Find a 90% confidence...
Let x = age in years of a rural Quebec woman at the time of her...
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 σ2 = 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 = 3.1. Use a 5% level of significance to test the claim that the current variance is less than 5.1. Find a 90% confidence...
Let x represent the number of mountain climbers killed each year. The long-term variance of x...
Let x represent the number of mountain climbers killed each year. The long-term variance of x is approximately σ2 = 136.2. Suppose that for the past 12 years, the variance has been s2 = 109.2. Use a 1% level of significance to test the claim that the recent variance for number of mountain-climber deaths is less than 136.2. Find a 90% confidence interval for the population variance. (a) What is the level of significance? State the null and alternate hypotheses....
A transect is an archaeological study area that is 1/5 mile wide and 1 mile long....
A transect is an archaeological study area that is 1/5 mile wide and 1 mile long. A site in a transect is the location of a significant archaeological find. Let x represent the number of sites per transect. In a section of Chaco Canyon, a large number of transects showed that x has a population variance σ2 = 42.3. In a different section of Chaco Canyon, a random sample of 24 transects gave a sample variance s2 = 45.1 for...
Let x represent the average annual salary of college and university professors (in thousands of dollars)...
Let x represent the average annual salary of college and university professors (in thousands of dollars) in the United States. For all colleges and universities in the United States, the population variance of x is approximately σ2 = 47.1. However, a random sample of 19 colleges and universities in Kansas showed that x has a sample variance s2 = 77.0. Use a 5% level of significance to test the claim that the variance for colleges and universities in Kansas is...
Let x represent the average annual salary of college and university professors (in thousands of dollars)...
Let x represent the average annual salary of college and university professors (in thousands of dollars) in the United States. For all colleges and universities in the United States, the population variance of x is approximately σ2 = 47.1. However, a random sample of 20 colleges and universities in Kansas showed that x has a sample variance s2 = 84.0. Use a 5% level of significance to test the claim that the variance for colleges and universities in Kansas is...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT