Question

In: Statistics and Probability

Why is important to perform a hypothesis test about a standard deviation?

Why is important to perform a hypothesis test about a standard deviation?

Solutions

Expert Solution

Explanation:

Knowing the mean of a population is important, but just as important is the accuracy and precision of your measurement. If you design a machine to fill 20 oz. soda bottles, you may find that the actual sample mean is  19.8oz±0.3oz .Great.

But margins of error are calculated from standard deviations, not the mean. How do you know the margin of error is 0.3 oz and not 3.0 oz? If you can't predict your standard deviation within a given interval, i.e. if your standard deviation is not accurate, your margin of error will be inaccurate.

 

It's important to not only estimate the population mean, but having a low margin of error for the standard deviation will help you make that prediction with a lower amount of error.


Precision is as important as accuracy.

Related Solutions

The Canadian government would like to test the hypothesis that the standard deviation for the hourly...
The Canadian government would like to test the hypothesis that the standard deviation for the hourly wage for men is equal to the standard deviation for the hourly wage for women. The sample size for men is 11 with sample standard deviation 2.25 and the sample size for women is 9 with standard deviation 3.75. Assume that hourly wages are normally distributed. a) What are the parameters of interest? b) Define the null and alternative hypothesis. c) What is the...
The federal government would like to test the hypothesis that the standard deviation for the age...
The federal government would like to test the hypothesis that the standard deviation for the age of men filing for Social Security is higher than the standard deviation for the age of women. The following table summarizes sample statistics from each population. Women Men Sample standard deviation 2.4 years 3.4 years Sample size 24 20 The test statistic for this hypothesis test would be ________. 2.01 4.87 5.60 7.74 A chocolate chip cookie producer claims that its cookies average 3...
Sony would like to test the hypothesis that the standard deviation for the age of PlayStation...
Sony would like to test the hypothesis that the standard deviation for the age of PlayStation users is higher than the standard deviation for the age of Xbox users. the following table summarizes sample statistics from each population. PlayStation Xbox Sample Standard Deviation 4.3 years 4.9 years Sample size 25 28 using a= 0.05, the conclusion for this hypothesis test would be that because the test statistics is A) more than the critical value, we reject the null hypothesis and...
Why is Cohen's d an important statistic to compute for a hypothesis test?
Why is Cohen's d an important statistic to compute for a hypothesis test?
Why is it important to calculate standard deviation for an investment? An investment portfolio is a...
Why is it important to calculate standard deviation for an investment? An investment portfolio is a group of investments. Why is it important to create an investment portfolio? (Hint: standard deviation) What is the optimal number of stocks in an investment portfolio? Is there any benefit to owning 100 individual stock positions?
Thinking about the Ho and Ha, what kind of hypothesis test will you have to perform...
Thinking about the Ho and Ha, what kind of hypothesis test will you have to perform if you want to see the influence of the single IV on the DV: One-tailed test (left) One-tailed test (right) Two-tailed test 2. Why is the adjusted coefficient of determination different from the regular R2.
A) Test these hypothesis by calculating the p value given that xbar=99, n=100, and standard deviation...
A) Test these hypothesis by calculating the p value given that xbar=99, n=100, and standard deviation =8. Ho: mu=100 H1: mu does not equal 100 B) repeat part a with n=50 C) repeat part a with n=20 D) what is the effect on the value of the test statistic and the p value of the test when the sample size decreases? PLEASE DO NOT USE MINITAB. YOU MAY USE EXCEL OR DO IT MANUALLY.
Design an experiment in which you would perform some sort of hypothesis test about frequencies. For...
Design an experiment in which you would perform some sort of hypothesis test about frequencies. For your chosen experiment, explain your entire experimental design. What is your population of interest? How are you going to randomly sample the pop? How many replicates will you collect? What will be the form of the data you collect and what test will you perform? What is your null and alternative hypothesis?
Using the data below, perform descriptive statistics analyses (mean, standard deviation, variance) for the brothers’ test....
Using the data below, perform descriptive statistics analyses (mean, standard deviation, variance) for the brothers’ test. Then, perform an Analysis of Variance (ANOVA) to determine if there is a significant difference between the brothers’ scores. Note: You may use Excel on your own or make an appointment to perform the test in SPSS Test Chapter 1, 2, 3&4 5 6 7 8&9 10 11&12 13 14 Chapter 1, 2, 3&4, 5, 6, 7, 8&9, 10, 11&12, 13, 14 (Jim) 85,...
Perform the appropriate Hypothesis Test for the following (Be sure to have a null hypothesis (H0)...
Perform the appropriate Hypothesis Test for the following (Be sure to have a null hypothesis (H0) and alternate hypothesis; (H1). Explain how to find test statistic and P-value on the calculator; also Interpret the results (i.e. Reject or Fail to Reject H0), (Is or Is not significant evidence to support the claim H1). You want to see if all three college algebra classes have the same mean. Use the following data to test your claim at a .01 significance level....
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT