A sleep center hypothesizes that people who sleep only four hours will score lower than people who sleep for eight hours on a cognitive skills test. The center recruited 20 participants and split them into two groups, giving one group 8 hours of sleep and the other only 4 hours. The following morning, the CAT (Cognitive Ability Test) was conducted, with scores ranging from 1-9, 9 being the best score. Use this information to answer questions . CAT Scores Group X: Eight hrs sleep 4 7 9 4 3 3 8 6 3 7 Group Y: Four hrs sleep 7 8 1 4 2 3 5 2 7 4 Conduct the following hypothesis test: - A one-tail T-test for a two-sample difference in means at the 95% confidence level - with Null Hypothesis that the Group X mean CAT score is equal to the Group Y mean CAT score - and with Alternate Hypothesis that the Group X mean CAT score is greater than the Group Y mean CAT score a). Calculate the mean and standard deviation of the scores for each group. (10%)

b)Using the correct degrees of freedom (df = group X size + group Y size ̶ # of groups), the correct number of tails, and at the correct confidence level, determine the critical value of t. (10%)

c). Explain under which scenarios using a pooled variance be inadvisable, then, calculate the pooled variance (formula for S2 is on page 379) for the groups. (10%)

d). Calculate the test statistic, Ttest (formula for t is on page 380). (10%)

e). The sleep center’s statistician tells you that the p-value for the test is 0.1535. Summarize the result of the study. Compare the mean scores in each group. Compare the test statistic to the critical value. Compare the p-value to alpha. Do you find a statistically significant difference between Group X and Group Y on cognitive test performance? Is there a meaningful/practical difference? Explain your decisions and Justify your claims

The ability of a mouse to recognize the odor of a potential predator is essential to the mouse’s survival. Typically, the source of these odors are major urinary proteins (Mups). 30% of lab mice sells exposed to chemically produced cat Mups responded positively (i.e. recognized the danger of the lurking predator). Consider a sample of 100 lab mice cells, each exposed to chemically produced cat MUPS. Let X represents the number of cells that respond positively.

a) Explain why the probability distribution of X can be approximated by the binomial distribution.

b) Find E(X) and interpret its value, practically.

c) Find the variance of X.

d) Give an interval that is likely to contain the value of X (2 st. dev around the mean).

e) How likely is it that less than half of the cells respond positively to cat Mups?

Suppose the following data were collected from a sample of 1515 houses relating selling price to square footage and the architectural style of the house. Which of the following is the best equation to use relating the selling price of a house to square footage and the style of the house?

Copy Data

Twenty laboratory mice were randomly divided into two groups of 10. Each group was fed according to a prescribed diet. At the end of 3 weeks, the weight gained by each animal was recorded. Do the data in the following table justify the conclusion that the mean weight gained on diet B was greater than the mean weight gained on diet A, at the α = 0.05 level of significance? Assume normality. (Use Diet B - Diet A.)

Diet A 5 13 9 8 10 14 5 8 7 5

Diet B 15 10 11 13 16 11 20 11 10 13

(a) Find t. (Give your answer correct to two decimal places.)

(ii) Find the p-value. (Give your answer correct to four decimal places.)

Is there a way to do this problem on a TI-84 Plus calculator? If so can you please break down the steps in getting the answers on the calculator? Thank you!

Which of the following distribution-free tests has the lowest efficiency rating compared to its

parametric counterpart?

A) Kruskal-Wallis test

B) Wilcoxon rank-sum test

C) Wilcoxon signed-ranks test

D) rank correlation test

1)Assume that the service life in years of a semiconductor is a random variable that has the Weibull distribution with alpha = 5 and beta = 3. What is the probability that a semiconductor like that will still be in operational condition between 3.7 and the 5 years?

2)Assume that the service life in years of a semiconductor is a random variable that has the Weibull distribution with alpha = 2 and beta = 4. What is the probability that a semiconductor like that will still be in operational condition until 4.9 years ?

1. *The following another set of data that looking at how long it takes to get to work. Let x= commuting distance (miles) and y= commuting time (minutes)

1. Give a scatterplot of this data and comment on the direction, form and strength of this relationship.
2. Determine the least-squares estimate equation for this data set.
3. Give the r², comment on what that means.
4. Give the residual plot based on the least-squares estimate equation.
5. Test if this least-squares estimate equation specify a useful relationship between commuting distance and commuting time.

answer all questions

Suppose that independent trials, each of which is equally likely to have any of m possible outcomes, are performed until the same outcome occurs k consecutive times. If N denotes the number of trials show that, E[N]=(m^k - 1)/(m-1)

In studies for a​ medication, 9 percent of patients gained weight as a side effect. Suppose 542 patients are randomly selected. Use the normal approximation to the binomial to approximate the probability that ​(a) exactly 42 patients will gain weight as a side effect. ​(b) 42 or fewer patients will gain weight as a side effect. ​(c) 56 or more patients will gain weight as a side effect. ​(d) between 42 and 65​, ​inclusive, will gain weight as a side effect. ​(a) ​P(Xequals42​)equals nothing ​(Round to four decimal places as​ needed)

The Australian Medical Association believed that the Health Minister's recent statement claiming that 75% of doctors supported the reforms to Medicare was incorrect. It thought that the actual support for the reforms was lower than this. The Association's President suggested the best way to test this was to survey 150 members, selected through a random sample, on the issue. She indicated that the Association would be prepared to accept a Type I error probability of 0.05.

1. State the direction of the alternative hypothesis for the test. Type gt (greater than), ge (greater than or equal to), lt (less than), le (less than or equal to) or ne (not equal to) as appropriate in the box.

2. State, in absolute terms, the critical value as found in the tables in the textbook.

3. Determine the lower boundary of the region of non-rejection in terms of the sample proportion of respondents (as a % to two decimal places) in favour of the reforms. If there is no (theoretical) lower boundary, type lt in the box.

4. Determine the upper boundary of the region of non-rejection in terms of the sample proportion of respondents (as a % to two decimal places) in favour of the reforms. If there is no (theoretical) upper boundary, type gt in the box.

5. If 102 of the survey participants indicated support for the reforms, is the null hypothesis rejected for this test? Type yes or no.

6. Disregarding your answer for 5, if the null hypothesis was rejected, could the Association claim that the Health Minister's assertion is incorrect at the 5% level of significance?

.

Suppose that a publisher conducted a survey asking adult consumers the number of fiction paperback books they had purchased in the previous month. The results are summarized in the Table 2.83.

Table 2.83

1. Are there any outliers in the data? Use an appropriate numerical test involving the IQR to identify outliers, if any, and clearly state your conclusion.
2. If a data value is identified as an outlier, what should be done about it?
3. Are any data values further than two standard deviations away from the mean? In some situations, statisticians may use this criteria to identify data values that are unusual, compared to the other data values. (Note that this criteria is most appropriate to use for data that is mound-shaped and symmetric, rather than for skewed data.)
4. Do parts a and c of this problem give the same answer?
5. Examine the shape of the data. Which part, a or c, of this question gives a more appropriate result for this data?
6. Based on the shape of the data which is the most appropriate measure of center for this data: mean, median or mode?

Mention the eleven (11) Root Cause Analysis Tools and describe what is the purpose of each one.

The College Board provided comparisons of Scholastic Aptitude Test (SAT) scores based on the highest level of education attained by the test taker's parents. A research hypothesis was that students whose parents had attained a higher level of education would on average score higher on the SAT. The overall mean SAT math score was 514.† SAT math scores for independent samples of students follow. The first sample shows the SAT math test scores for students whose parents are college graduates with a bachelor's degree. The second sample shows the SAT math test scores for students whose parents are high school graduates but do not have a college degree.

c) find the value of the test statistic. (round your answer to three decimal places)

d) compute the p-value for the hypothesis test ( round your answer to four decimal places) p value=

Avoiding an accident while driving can depend on reaction time. That time, measured from the time the driver first sees the danger until the driver gets his/her foot on the brake pedal, can be described by a normal model with mean 1.9 seconds and standard deviation 0.13 seconds. Use the 68-95-99.7 rule (NOT a z table) to answer the following questions. The pictures of the 68-95-99.7 rule at this link might help.
http://www.oswego.edu/~srp/stats/6895997.htm

What percentage of drivers have a reaction time more than 2.16 seconds?

________%

What percentage of drivers have a reaction time less than 1.77 seconds?
________%

What percentage of drivers have a reaction time less than 2.03 seconds?
________%