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?
________%

Use Minitab to answer the questions. Make sure to copy all output from the Minitab:

Followings Tables shows previous 11 months stock market returns.

1. Let consider we know the variance of monthly return for all stock were 25 percent in 2008, perform the following hypothesis for each index:

Ho :  µ = -5

Ha :  µ ≠ -5

2. Considering the population variance is unknown, perform a hypothesis test if the average stock return is 0 or not for each index:

Ho :  µ = 0

Ha :   µ ≠  0

3. Perform following hypothesis based on all assumption we had in 2)

Ho :  µ ≥ -3

Ha :   µ <  -3

4. Let’s consider the population mean of SP500 as µ1 and that of DJIA as µ2 while none of population variance is known. Test following hypothesis:

  Ho : µ1  =  µ2

Ha :   µ1 ≠  µ2

5. Let’s consider the population variance of SP500 as σ²₁and that of DJIA as σ²₂, and none of them are known. Test following hypothesis:

  Ho :  σ²₁  =  σ²₂

  Ha :  σ²₁≠  σ²₂

6. Perform the following hypothesis test

  Ho :  σ²₁  ≤  σ²₂

  Ha :  σ²₁>  σ²₂

a busy social life has been found to increase happiness in participants who are experincing low levels of stress, but decrease happoiness in participants who are experiencing high levels of stress .what is this an example of? a)moderation b)mediation c)neither moderation nor mediation d)semi partial correlation

2)what is the sobel test used for? A) To acssess the significant of the direct effect in moderation analysis .B) To assess the significant in mediation. C) to assess the significant of the interaction effect in moderation analysis. D)to assess the significant of he indiect effect in mediation analysis

Queueing Theory

apply elementary queueing theory equations to compute statistics for the various scheduling systems

assume exponential inter-arrival and service time distributions

At the South Loop Oil 'n Lube, a new customer arrives for an oil change every 20 minutes, and is annoyed to find, on average, 3 customers ahead of him (including the one being serviced).

How much longer, typically, will it take for the current customer to finish his oil change?

After that, how much longer will the new customer have to wait to complete his own oil change?

1. The Gallup Poll asked a probability sample of 2500 U.S. adults whether they used a credit card to pay for groceries that week. Suppose that 25% of the adult population did. We would like to know the probability that an SRS of size 2500 would come within plus or minus 2 percentage points of this true value.
   1. If p-hat is the proportion of the sample who did use a credit card to pay for groceries, what is the mean of p-hat? (2 points)
      
      
   2. What is the standard deviation of p-hat? (2 points)
      
      
   3. Explain why you can use the formula for the standard deviation of p-hat in this setting.(check that the population is at least 10 times larger than the sample) (2 points)
      
   4. Check that you can use the normal approximation for the distribution of p-hat.(2 points)
      
      
   5. Find the probability that p-hat takes a value between 0.23 and 0.27. (4 points)

The daily intake of calcium was measured (in milligrams) from a random sample of 16 women between the ages of 20 and 29. The sample mean and sample standard deviation of the observed data were calculated to be 866.8 and 255.5, respectively. (4 decimals places)

1. Conduct a 95% confidence interval for the population mean daily intake of calcium. State the lower bound.

2. Conduct a 95% confidence interval for the population mean daily intake of calcium. State the upper bound.

3. What is the margin of error for the above confidence interval

Example Problem: [Ch 9, Q36] Consider the following hypothesis test: ?0: ? ≥ 0.75; ??: ? < 0.75. A sample of 300 items was selected. Using ? = 0.05, conduct a hypothesis test and state your conclusions for the following scenarios: ?̅ = 0.68; ?̅ = 0.72; ?̅ = 0.70; ?̅ = 0.77.

Bob Michels owns a business in an emerging agricultural market, medicinal cannabis. He is interested in running a regression analysis with fertilizer potency as the dependent variable and manufacturing process temperature as the predictor variable. After taking a sample of 25 batches and recording these two variables, Bob developed the following results:

Potency = -8.78 + .48897 TEMP

(.0792)

S_e = 3.473 SS(total)= 737.73

Potency is the percent of maximum fertilizer potency

Temp is the temperature in degrees in Fahrenheit.

Interpret the regression coefficient.

Test whether ther is a positive linear relationship between potency and Temp. Use alpha = .05

Develop the Mission ANOVA table

It is known that 5% of all laptops from a certain manufacturer have a certain defect.A random sample of 20 laptops from this manufacturer is selected.a)What is the probability that no laptops in the sample have defect?.b)What is the probabilty that exactly two laptops in the sample have defect?.c)What is the probabilty that atmost 2 laptops in the sample have the defect?.Let X denote the number of defective laptops in a sample .what is the expected value of X , E[X]?.and Laptops from this manufacturer are sold in batches of 12 and a batch is deemed to be unsatisfactory if it contains 2 or more laptops with defect.If 5 batches are selected at random ,what is the probability that at least 2 of them are deemed unsatisfactory?