The fact that confidence intervals and hypothesis tests are both used to determine statistical significance means that they can be used interchangeably and give us the same information.

Rationale:

A researcher wants to know if the news station a person watches is a factor in the amount of time (in minutes) that they watch. The table below shows data that was collected from a survey.

Assume that all distributions are normal, the three population standard deviations are all the same, and the data was collected independently and randomly. Use a level of significance of α=0.01α=0.01.

H0: μ1=μ2=μ3H0: μ1=μ2=μ3
H1:H1: At least two of the means differ from each other.

1. For this study, we should use Select an answer TInterval 2-SampTTest T-Test ANOVA 1-PropZInt 2-SampTInt 1-PropZTest χ²-Test 2-PropZInt 2-PropZTest χ²GOF-Test
2. The test-statistic for this data =  (Please show your answer to 3 decimal places.)
3. The p-value for this sample =  (Please show your answer to 4 decimal places.)
4. The p-value is Select an answer less than (or equal to) alpha greater than alpha  αα
5. Base on this, we should Select an answer accept the null hypothesis fail to reject the null hypothesis reject the null hypothesis  hypothesis
6. As such, the final conclusion is that...
   • There is insufficient evidence to support the claim that station is a factor in the amount of time people watch the news.
   • There is sufficient evidence to support the claim that station is a factor in the amount of time people watch the news.

Do the following sets of vectors span R^3?

1) [1,3,1], [3,9,4], [8,24,10], [-10,-30,-13]

2) [1,2,3], [-1,-2,-4], [1,2,2]

3) [-1,-3,-1], [-4,-12,-3]

4)[1,2,-2], [7,5,7], [-4,-1,-11]

Use the following data set to calculate the regression equation. What would you estimate the happiness rating for someone who has 5 children to be?

What are two ways to test the equality of population variances? Explain in detail.

Positive, Negative, or zero. Suppose you are looking at three separate relationships that are modeled by linear functions. One linear model has a positive slope, one has a negative slope, and one has a slope of zero. What do these slopes tell you about the relationships they model? Find practical examples of each of the three.

Using the data from your organization, identify an example where the quantitative Statistical Quality Control could assist with a decision.

a)      Define the states of problem.

b)      Organize data in a Control Chart for the Mean with UCL and LCL charts included.

c)      Organize data in a Control Chart for the Range with UCL and LCL charts included.

There are 723 seniors at a large high school.

(a) Explain how you would use a random number table to select a random sample of 30 seniors. Explain your method clearly! I should be able to hand you directions to Mr. Carter and he should be able to select the sample.

(b) Using the random digits below, select the first five seniors using your method from Part (a).

73190 32533 04470 29669 84407 90785 65956 86382

95857 07118 87664 92099 58806 66979 98624 84826

1. A company make profits of $22,000 on each of its five low end products $50,000 for each of the two mid end ones and $270,000 from one top product. The number of products contributing less than the mean profit is

a) 4 b) 7 c) 5 d) 6 e) 0

2. Of most of the prices in a large data set are of approximately the same magnitude except for a few observations that are quite a bit larger, how would the mean and median of the data set compare and what shape would a histogram of the data set have?

a) the mean would be equal to the median and the histogram would be symmetrical

b) the mean would be smaller than the median and the histogram would be skewed with a long right tail.

c) the mean would be larger than the median and the histogram would be skewed with a long left tail

d) the mean would be larger than the median and the histogram would be skewed with a long right tail

e) the mean would be smaller than the median and the histogram would be skewed with a long left tail

3. What are the assumptions behind the two pricing strategies and what are their strength and weakness?

4. Suppose a university decides to raise tuition fees to increase the total revenue it receives from students. This strategy will work if the demand for education at the university is..

a) unit elastic b) inversely related to price c) elastic d) inelastic e) perfectly elastic

4-2.5 In a class of 50 students, the result of a particular examination is a true mean of 70 and a true variance of 12. It is desired to estimate the mean by sampling, without replacement, a subset of the scores.

a) Find the standard deviation of the sample mean if only 10 scores are used.

b) How large should the sample size be for the standard deviation of the sample mean to be one percentage point (out of 100)?

c) How large should the sample size be for the standard deviation of the sample mean to be 1 % of the true mean?

I don't think need more informations in case this q from (Cooper - Probabilistic Methods of Signal and System Analysis, 3rd Ed) page 185

For this assignment, you will create a cross tabs and conduct a chi-square test of independence. Begin by asking some of your friends or acquaintances (you'll need both males and females) what their favorite pet type is, out of a dog, a cat, a hamster, or a lizard. Then, create a cross tabs (you can use the following template) with this information. Crosstabs: Gender and Favorite Pet Type Dog Cat Hamster Lizard Total Female Male Total Once you have completed a cross tabs, create a report of 1-2 pages in which you address the following: Explain whether or not you expect there to be a significant relationship between these variables based on the information you've collected. Then, conduct a chi-square test for your data. Use the appropriate table in your textbook to determine if the result is significant. Explain what this implies for the variables.

For this discussion, you will create an example to which the chi-square test of independence could be applied. Develop a main response in which you address the following:

• Identify two categorical variables for which a chi-square test of independence could be conducted.
• Describe the categories of each.
• Explain why these would be appropriate for this test.
• Predict whether or not the chi-square test result would be significant, and what this would imply about the variables.

1. Test the claim about the population mean, ?, at the level of significance, ?. Assume the population is normally distributed.

Claim: ? ≤ 47, ? = 0.01, ? = 4.3 Sample statistics: ?̅ = 48.8, ? = 40

A. Fail to reject ?0. There is enough evidence at the 1% significance level to support claim.

B. Not enough information to decide.

C. Reject ?0. There is enough evidence at the 1% significance level to reject the claim.

2.

Use the following information to answer questions 28, 29, and 30. The heights in inches of 10 US adult males are listed below.

70 72 71 70 69 73 69 68 70 71

a) Determine the range.

b) Determine the standard deviation.

c) Determine the variance.

3. The weights in pounds of 30 preschool children are listed below. Find the five number summary of the data set.

25 25 26 26.5 27 27 27.5 28 28 28.5

29 29 30 30 30.5 31 31 32 32.5 32.5

33 33 34 34.5 35 35 37 37 38 38

4. A manufacturer receives an order for light bulbs. The order requires that the bulbs have a mean life span of 850hours. The manufacturer selects a random sample of 25 light bulbs and finds they have a mean life span of 845 hours with a standard deviation of 15 hours. Assume the data are normally distributed. Using a 95% confidence level, test to determine if the manufacturer is making acceptable light bulbs and include an explanation of your decision.

5. A manufacturer of golf equipment wishes to estimate the number of left-handed golfers. How large of a sample is needed in order to be 95% confident that the sample proportion will not differ from the true proportion by more than 4%.

6.

A local group claims that the police issue at least 60 speeding tickets a day in their area. To prove their point, they randomly select one month. Their research yields the number of tickets issued for each day. The data are listed below. Assume the population standard deviation is 12.2 tickets. At ? = 0.01, test the group’s claim. Make sure to state your conclusion regarding the claim with your reasoning.

70 48 41 68 69 55 70 57 60 83 32 60 72 58 88 48

59 60 56 65 66 60 68 42 57 59 49 70 75 63 44

7. A local politician, running for reelection, claims that the mean prison time for car thieves is less than the required 4 years. A sample of 80 convicted car thieves was randomly selected, and the mean length of prison time was found to be 3.5 years. Assume the population standard deviation is 1.25 years. At ? = 0.05, test the politician’s claim. Make sure to state your conclusion regarding the claim with your reasoning.

What is the root-sum-square uncertainty model?

The distribution of Master’s degrees conferred by a university is listed in the table.

What is the probability that a randomly selected student graduating with a Master’s degree has a major of Education or a major of Engineering?

A. 0.371 B. 0.720 C. 0.390 D. 0.280

2.

The data below are the final exam scores of 10 randomly selected statistics students and the number of hours they studied for the exam.

A). Calculate the correlation coefficient.

B). Find the equation of the regression line.

C). Use the regression equation to predict the test score of a student who studied for 5.5 hours.

3. Find the ?-score for which 70% of the distribution’s area lies to its right.

A. -0.52 B. -0.98 C. -0.48 D. -0.81

4. A group of 49 randomly selected students has a mean age of 22.4 years. Assume the population standard deviation is 3.8. Construct a 98% confidence interval for the population mean.

A. (20.3, 24.5) B. (18.8, 26.3) C. (21.1, 23.7) D. (19.8, 25.1)

5.Use fundamental counting principle to determine how many license plates can be made consisting of 3 different letters followed by 2 different digits.

A. 1,757,600 B. 175,760 C. 100,000 D. 1,404,000

6. A group of students were asked if they carry a credit card. The responses are listed in the table.

If a student is selected at random, find the probability that he/she owns a credit card given that the student is a freshman.

A. 0.400 B. 0.615 C. 0.667 D. 0.333

7. Use the standard normal distribution to find ?(−2.50 < ? < 1.50).

A. 0.8822 B. 0.5496 C. 0.6167 D. 0.9270

8.

The number of home runs that Barry Bond hit in the first 18 years of his major league career are listed.

16 25 24 19 33 25 37 41 37

25 42 40 37 34 49 73 46 45

A). Find the mean.

B). Find the median.

C). Find the mode.