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# Two hypothesis testing questions

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1. Suppose that the mean of the annual return for common stocks from 2000 to 2012 was 14.37%, and the standard deviation of the annual return was 35.14%. Suppose also that during the same 12-year time span, the mean of the annual return for long-term government bonds was 0.6%, and the standard deviation was 2.1%. The distributions of annual returns for both common stocks and long-term government bonds are bell-shaped and approximately symmetric in this scenario. Assume that these distributions are distributed as normal random variables with the means and standard deviations given previously.
a Find the probability that the return for common stocks will be greater than 16.32%.
b. Find the probability that the return for common stocks will be greater than 5.89%.
c. Find the probability that the return for common stocks will be less than 14.37%.

2. The management of a computer software company is considering relocating the corporate office (A) to a new location out of state, office (B). The management is concerned that the commute times of the employees to the new office (B) might be too long. The company decides to survey a sample of employees at other companies in the same office (A) to see how long these employees are commuting to the office. A sample of 23 employees indicated that the employees are commuting X (bar) = 33 minutes and s = 1 minute, 45 seconds.
1. a. Using the 0.01 level of significance, is there evidence that the population mean is above 32 minutes?
2. b. What is your answer in (a) if X (bar) = 37 minutes and s = 27 minutes?
3. c. Look at your answers for a and b above and discuss what you can learn from the results about the effect of a large standard deviation.

https://brainmass.com/statistics/frequentist-inference/two-hypothesis-testing-questions-571588

#### Solution Preview

1. Suppose that the mean of the annual return for common stocks from 2000 to 2012 was 14.37%, and the standard deviation of the annual return was 35.14%. Suppose also that during the same 12-year time span, the mean of the annual return for long-term government bonds was 0.6%, and the standard deviation was 2.1%. The distributions of annual returns for both common stocks and long-term government bonds are bell-shaped and approximately symmetric in this scenario. Assume that these distributions are distributed as normal random variables with the means and standard deviations given previously.
a Find the probability that the return for common stocks will be greater than 16.32%.
Since distribution of annual returns for common stocks is bell-shaped and approximately symmetric in this scenario, it is normally ...

#### Solution Summary

The solution gived detailed steps on hypothesis testing. All formula and calculations are shown and explained.

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## Multiple choice questions in statistics-hypothesis, t statistic , p-value, two tailed test, population standard deviation, equality of the variance, F statistic, power of test, Kimberly Clark Corporation , related populations

I'm having trouble understanding the following question can you please explain?

1) The owner of an Internet video supplier, Netflix, has conducted a study of habits of online customers. In particular she wants to estimate the average number of videos checked out each month. Before she can determine the sample size she will need, she needs to make an estimate of the standard deviation. On the basis of her past experience and judgment, she estimate that the standard deviation is equal to 12. Suppose that a pilot study of 15 online customers indicates a sample standard deviation of 9.25 videos. At 0.10 level of significance what are the critical boundaries for rejecting H : @=12
0
A)x2 <-6.571 or x2 >+ 6.571 (B) x2<-6.571 or x2 >+23.685 (C) x2 <-2.575 or x2 >+2.575(D) x2 <-23.865 or x2 > + 23.685

2) A survey claims that 9 out of 10 doctors recommend aspirin for their patient with headaches. To test this claim against the alternative that the actual proportion of doctors who recommend aspirin is less than 0.90, a random sample of 100 doctors results in 83 who indicate that they recommend aspirin. The value of the test statistic in this problem is approximately equal to:
A) -4.12 (B) -2.33 (C) -1.86 (D) -0.07

3) Using the table below, which of the following is the correct calculation of the t statistic needed to test the null hypothesis that there is no difference in the average price of items at two stores?

ITEM STORE A STORE B
1gal milk \$2.94 \$3.33
Tide Detergent, jumbo box 7.58 8.79
3lbs. Fuji apple 2.41 2.97
Oreo 3.16 3.39
1lb T-bone 5.77 7.99
Tropicana OJ, 64 oz 3.67 3.99
Huggies 24 pack 7.76 7.99
1pint Breyers ice cream 2.94 3.19
64oz Colgate toothpaste 2.08 2.19

A) -0.011 (B) -0.541 (C) -1.746 (D) -2.686

4) If the p value is less than a in two-tailed test
A) the null hypothesis (B) the null hypothesis should be rejected (C) a one-tailed test should be used(D) no conclusion should be reached

5) Calculate the test statistic for the internet video supplier's research in Problem #12 above. The test statistic, x2 =
A) Cannot be computed because the population standard deviation is not known (B) 8.913 (C) 8.319 (D) -8.913

6) An upholstery business is studying differences between two of its major outlet stores in the time its take customers to receive furniture that was custom ordered. The following data shows a sample of delivery times for the most popular types of furniture.

STORE A STORE B
X 34.3 days 43.7 days
S 2.4 days 3.1 days
n 41 31

Which of the following is the correct F statistic for testing the equality of the variance for these two sample.
A) 0.599 (B) 0.774 (C) 0.935 (D) 1.018

7) Assembly line worker are randomly assigned to two groups with 21 workers in each group. Each group receive a different training program and then their scores on an assembly task are compared. The F statistic for the variance in 2 groups is 0.178. Using a 0.05 level of significance, what are the critical values for rejecting the null hypothesis that there is no difference in the variance of these two population?
A) If F < 2.46 and F>0.407, rejects H ( B) if F >2.46 or F< 0.407, rejects H
0 0
C) If F < 2.12 and F> 0.472 rejects H (D) If > 2.12 or F< 0.472 rejects H
0 0

8) For a given sample size n, if the level of significance (a) is decreased, the power of the test :
A) will increase (B) will decrease (C) will remain the same (D) cannot be determined

9) In what type of test is the variable of interest the difference between the value of the observation rather than the observation themselves.
A) A test for equality of variance from two independent population (B) A test for difference between the means of two related population (C) A test for the difference between the means of two independent population (D) all of the above

10) In testing for differences between the means of two related populations, the null hypothesis is:
A) H: u =2 (B) H: u < 0 (C) H : u (D) H : u = 0
0 D 0 D 0 D 0 D

11) How many Kleenex should the Kimberly Clark Corporation package of issue contain? Researchers determined that 60 tissue is the average number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissue used during a cold:-- = 52,s=22. Using the sample information
X
provided, calculate the value of the test statistic.
A) t=-0.3636 (B) t=-36.3636(C)t=-3636.3636 (D) t=-3.6364

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