A researcher is interested in determining if the attitude about homosexual marriages is dependent on region. In order to do the Chi-Square association test, she ran analysis with Minitab and came up with the contingency table that summarizes the actual observations and the expected observations. α=0.05.

Report your test statistic and your conclusion .

Round your test statistic to the nearest decimal. Report your conclusion as D (dependent) or I (independent)

A random rearrangement doe not separate out between repeated letters. Consider word CHRISTMASTIME.

a) What's the expected # vowels in first three letters of random rearrangement of CHRISTMASTIME?

b) What's probability that all the S's happen before all the I's in random rearrangement of CHRISTMASTIME?

c) What's probability that word CHRIST happens in consecutive letters of uniform rearrangement of CHRISTMASTIME?

Anderson et al. (1990) studied the effect of diet on the level of low-density lipoprotein (LDL, the “bad” cholesterol) for a group of men with hypercholesterolemia. Half the subjects were given a diet that included corn flakes and the other half were given a diet that included oat bran. LDL was then measured after two weeks. Subjects were then crossed-over to the alternative diet for an additional two weeks. LDL was measured again. The LDL measurements are shown below. Test the null hypothesis that the mean difference in LDL points to a population in which the difference is zero, suggesting that the one diet is no better than the other for controlling LDL. What does the result suggest? (this can be answered in one or two sentences)

LDL (in mmol/L) -------- Corn Flakes 4.61 6.42 5.40 4.54 3.98 3.82 5.01 4.34 3.80 4.56 5.35 3.89

Oat Brab 3.84 5.57 5.85 4.80 3.68 2.96 4.41 3.72 3.49 3.84 5.26 3.73 -----------------------

I can't figure out how to create the decision tree with the sending a messaged situation!

The crew of Endurance can visit two planets (Mann’s and Edmunds’). They can choose to visit neither planets, one of the two planets, or both planets. The characteristics of Mann’s planet are below:

• 30% chance of finding a perfectly habitable planet

• can support all of Earth’s current population if it is

• can support none of Earth’s population if it is not

And the characteristics of Edmunds’ planet are below:

• 50% chance of finding a perfectly habitable planet

• can support 50% of Earth’s current population if it is (because it is not as large as Mann’s planet)

• can support 20% of Earth’s current population if it is not (because it is still partially habitable)

The crew also needs to decide when to send a message to Earth to let them know which planet to migrate to. The possible outcomes for the different time steps of when they send that message are below:

• If they send the message before visiting both planets, none of the Earth’s population would have perished on Earth before receiving that message.

• If they send the message after visiting only one planet (either one), 10% of the Earth’s population would have perished on Earth before receiving that message.

• If they send the message after visiting both planets, 25% of the Earth’s population would have perished on Earth before receiving that message.

What should the crew do to save as many of Earth’s population as possible? Specifically, which planet or planets should they visit, if any and in what order, and when should they send the message to Earth? Draw a decision tree to solve this problem.

There are 9 balls out of which one ball is heavy in weight and rest are of the same weight. In how many occurrences will you find the heavy ball?

4. The director of the Wisconsin Department of Business Licensing is looking for ways to improve employee productivity. Specifically, she would like to see an improvement in the percentage of applications that employees process correctly. The director randomly selects 50 employees and gather data on the percentage of applications each one correctly processed last month. On the recommendation of a consultant, the director has these 50 employees complete a 3-day workshop on Proactive Synergy Restructuring Techniques. At the end of the month following the training, the director collects the application processing data for the same 50 employees. Help the director analyze these data by conducting a hypothesis test. From a statistical point of view, what can you tell the director?

The Heinlein and Krampf Brokerage firm has just been instructed by one of its clients to invest $250,000 of her money obtained recently through the sale of land holdings in Ohio. The client has a good deal of trust in the investment house, but she also has her own ideas about the distribution of the funds being invested. In particular, she requests that the firm select what- ever stocks and bonds they believe are well rated but within the following guidelines:

● Municipal bonds should constitute at least 20% of the investment.

● At least 40% of the funds should be placed in a combination of electronic firms, aerospace firms, and drug manufacturers.

● No more than 50% of the amount invested in municipal bonds should be placed in a high-risk, high-yield nursing home stock.

Subject to these restraints, the client’s goal is to maximize projected return on investments. The analysts at Heinlein and Krampf, aware of these guidelines, prepare a list of high-quality stocks and bonds and their corresponding rates of return:

(a) Formulate this portfolio selection problem using LP.

(b) Solve this problem.

According to the Carnegie unit system, the recommended number of hours students should study per unit is 2. Are statistics students' study hours more than the recommended number of hours per unit? The data show the results of a survey of 13 statistics students who were asked how many hours per unit they studied. Assume a normal distribution for the population. 3.1, 2.6, 2.9, 4.2, 3.9, 1.9, 0.6, 2.4, 0.8, 2.7, 4.3, 3.7, 2.1 What can be concluded at the α α = 0.05 level of significance? a.For this study, we should use Select an answer z-test for a population proportion t-test for a population mean b.The null and alternative hypotheses would be: H0: H0: ? p μ ? ≠ < = > H1: H1: ? μ p ? ≠ > < = c.The test statistic ? t z = (please show your answer to 3 decimal places.) d.The p-value = (Please show your answer to 4 decimal places.) e.The p-value is ? ≤ > α α f.Based on this, we should Select an answer fail to reject reject accept the null hypothesis. g.Thus, the final conclusion is that ... The data suggest the population mean is not significantly more than 2 at α α = 0.05, so there is sufficient evidence to conclude that the population mean study time per unit for statistics students is equal to 2. The data suggest that the population mean study time per unit for statistics students is not significantly more than 2 at α α = 0.05, so there is insufficient evidence to conclude that the population mean study time per unit for statistics students is more than 2. The data suggest the populaton mean is significantly more than 2 at α α = 0.05, so there is sufficient evidence to conclude that the population mean study time per unit for statistics students is more than 2. h.Interpret the p-value in the context of the study. There is a 2.53303373% chance that the population mean study time per unit for statistics students is greater than 2. There is a 2.53303373% chance of a Type I error. If the population mean study time per unit for statistics students is 2 and if you survey another 13 statistics students then there would be a 2.53303373% chance that the population mean study time per unit for statistics students would be greater than 2. If the population mean study time per unit for statistics students is 2 and if you survey another 13 statistics students then there would be a 2.53303373% chance that the sample mean for these 13 statistics students would be greater than 2.71. i.Interpret the level of significance in the context of the study. There is a 5% chance that the population mean study time per unit for statistics students is more than 2. There is a 5% chance that students just don't study at all so there is no point to this survey. If the population mean study time per unit for statistics students is 2 and if you survey another 13 statistics students, then there would be a 5% chance that we would end up falsely concuding that the population mean study time per unit for statistics students is more than 2. If the population mean study time per unit for statistics students is more than 2 and if you survey another 13 statistics students, then there would be a 5% chance that we would end up falsely concuding that the population mean study time per unit for statistics students is equal to 2.

Women are recommended to consume 1900 calories per day. You suspect that the average calorie intake is smaller for women at your college. The data for the 15 women who participated in the study is shown below: 1625, 1927, 1996, 1762, 1766, 1885, 2008, 1751, 1666, 1837, 1981, 1603, 1881, 1606, 1625 Assuming that the distribution is normal, what can be concluded at the α α = 0.05 level of significance? a.For this study, we should use Select an answer z-test for a population proportion t-test for a population mean b.The null and alternative hypotheses would be: H0: H0: ? μ p ? = > < ≠ H1: H1: ? μ p ? < > = ≠ c.The test statistic ? z t = (please show your answer to 3 decimal places.) d.The p-value = (Please show your answer to 4 decimal places.) e.The p-value is ? ≤ > α α f.Based on this, we should Select an answer reject accept fail to reject the null hypothesis. g.Thus, the final conclusion is that ... The data suggest the populaton mean is significantly less than 1900 at α α = 0.05, so there is sufficient evidence to conclude that the population mean calorie intake for women at your college is less than 1900. The data suggest the population mean is not significantly less than 1900 at α α = 0.05, so there is sufficient evidence to conclude that the population mean calorie intake for women at your college is equal to 1900. The data suggest that the population mean calorie intake for women at your college is not significantly less than 1900 at α α = 0.05, so there is insufficient evidence to conclude that the population mean calorie intake for women at your college is less than 1900. h.Interpret the p-value in the context of the study. If the population mean calorie intake for women at your college is 1900 and if you survey another 15 women at your college, then there would be a 0.7648994% chance that the sample mean for these 15 women would be less than 1795. If the population mean calorie intake for women at your college is 1900 and if you survey another 15 women at your college, then there would be a 0.7648994% chance that the population mean calorie intake for women at your college would be less than 1900. There is a 0.7648994% chance that the population mean calorie intake for women at your college is less than 1900. There is a 0.7648994% chance of a Type I error. i.Interpret the level of significance in the context of the study. If the population mean calorie intake for women at your college is less than 1900 and if you survey another 15 women at your college, then there would be a 5% chance that we would end up falsely concuding that the population mean calorie intake for women at your college is equal to 1900. There is a 5% chance that the population mean calorie intake for women at your college is less than 1900. If the population mean calorie intake for women at your college is 1900 and if you survey another 15 women at your college, then there would be a 5% chance that we would end up falsely concuding that the population mean calorie intake for women at your college is less than 1900. There is a 5% chance that the women at your college are just eating too many desserts and will all gain the freshmen 15.

W75A - Please answer in detail using EXCEL Function

T-test of 2 means (Similar to presentation in class; but in a different context)

              (Wednesday class)

              Researchers in Georgia take a sample of diameters from 30 old-growth pine trees growing on two separate and adjoining tracts of land, labeled north and south, to see if the trees are identical.   The data are shown in the Tables below and reproduced in the Excel answer workbook.

1. Using Excel’s t-test of two means, calculate the P-value of a two-tail taste to identify whether the mean tree diameter from the north tract and south tracts are identical or not at a 5% level of significance. (Round to four digits.) Make sure you state the null and alternative hypotheses, as well as a formal conclusion to your test. (The Excel answer workbook reminds you to do so!) Assume variances (and, therefore, standard deviations are not equal. (1 point)

(North)

              (South)

Problem 1:

Work through Example 13 (which starts on p. 36 of the lab manual) and then do the following using the data from Problem #1 above. (a) Find the p-value for the hypothesis test in Problem #1(a) above. (b) Construct a normal probability plot of the residuals which includes the p-value for the normality test (similar to Figure 9, p. 41 of the lab manual). Enter the p-value into the answer box. (c) Find the p-value for the hypothesis test of equality of population variances (using Bartlett's test).

B. The proportion of customers who are completely satisfied in a recent satisfaction survey of 300 customers at XYC Inc. is found to be 0.26. Test the hypothesis that the population proportion of customers who are completely satisfied is greater than 0.22 using the critical value approach and a 0.05 level of significance. e Test the hypothesis that the population proportion of customers who are completely satisfied is less than 0.30 using the p-value approach and a 0.05 level of significance. b. Test the hypothesis that the population proportion of customers who are completely satisfied is different from 0.24 using the p-value approach and a 0.05 level of significance. C.

If you have a chance please answer as many as possible, thank you and I really appreciate your help experts!

Question 16 2 pts

In a hypothesis test, the claim is μ≤28 while the sample of 29 has a mean of 41 and a standard deviation of 5.9. In this hypothesis test, would a z test statistic be used or a t test statistic and why?

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Question 17 2 pts

A university claims that the mean time professors are in their offices for students is at least 6.5 hours each week. A random sample of eight professors finds that the mean time in their offices is 6.2 hours each week. With a population standard deviation of 0.49 hours, can the university’s claim be supported at α=0.05?

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Question 18 2 pts

A credit reporting agency claims that the mean credit card debt in a town is greater than $3500. A random sample of the credit card debt of 20 residents in that town has a mean credit card debt of $3619 and a standard deviation of $391. At α=0.10, can the credit agency’s claim be supported?

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Question 19 2 pts

A car company claims that its cars achieve an average gas mileage of at least 26 miles per gallon. A random sample of eight cars from this company have an average gas mileage of 25.6 miles per gallon and a standard deviation of 1 mile per gallon. At α=0.06, can the company’s claim be supported?

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Question 20 2 pts

A researcher wants to determine if extra homework problems help 8^th
grade students learn algebra. One 8^th grade class has extra homework problems and another 8^th grade class does not. After 2 weeks, the both classes take an algebra test and the results of the two groups are compared. To be a valid matched pair test, what should the researcher consider in creating the two groups?

The manufacturer claims that your new car gets 31 mpg on the highway. You suspect that the mpg is a different number for your car. The 40 trips on the highway that you took averaged 28.7 mpg and the standard deviation for these 40 trips was 5.8 mpg. What can be concluded at the α α = 0.01 level of significance? a.For this study, we should use Select an answer z-test for a population proportion t-test for a population mean b.The null and alternative hypotheses would be: H0: H0: ? μ p ? ≠ = > < H1: H1: ? μ p ? > < = ≠ c.The test statistic ? t z = (please show your answer to 3 decimal places.) d.The p-value = (Please show your answer to 4 decimal places.) e.The p-value is ? ≤ > α α f.Based on this, we should Select an answer reject fail to reject accept the null hypothesis. g.Thus, the final conclusion is that ... The data suggest that the sample mean is not significantly different from 31 at α α = 0.01, so there is statistically insignificant evidence to conclude that the sample mean mpg for your car on the highway is different from 28.7. The data suggest that the population mean is not significantly different from 31 at α α = 0.01, so there is statistically insignificant evidence to conclude that the population mean mpg for your car on the highway is different from 31. The data suggest that the populaton mean is significantly different from 31 at α α = 0.01, so there is statistically significant evidence to conclude that the population mean mpg for your car on the highway is different from 31. h.Interpret the p-value in the context of the study. There is a 1.64116434% chance of a Type I error. If the population mean mpg for your car on the highway is 31 and if you take another 40 trips on the highway then there would be a 1.64116434% chance that the population mean would either be less than 28.7 or greater than 33.3. There is a 1.64116434% chance that the population mean mpg for your car on the highway is not equal to 31. If the population mean mpg for your car on the highway is 31 and if you take another 40 trips on the highway, then there would be a 1.64116434% chance that the sample mean for these 40 highway trips would either be less than 28.7 or greater than 33.3. i.Interpret the level of significance in the context of the study. There is a 1% chance that you own an electric powered car, so none of this matters to you anyway. If the population population mean mpg for your car on the highway is different from 31 and if you take another 40 trips on the highway, then there would be a 1% chance that we would end up falsely concluding that the population mean mpg for your car on the highway is equal to 31. There is a 1% chance that the population mean mpg for your car on the highway is different from 31. If the population mean mpg for your car on the highway is 31 and if you take another 40 trips on the highway, then there would be a 1% chance that we would end up falsely concluding that the population mean mpg for your car on the highway is different from 31.