Part 1

The systolic blood pressure of adults in the USA is nearly normally distributed with a mean of 120 and standard deviation of 23 .

Someone qualifies as having Stage 2 high blood pressure if their systolic blood pressure is 160 or higher.

a. Around what percentage of adults in the USA have stage 2 high blood pressure? Give your answer rounded to two decimal places. ____ %

b. If you sampled 2000 people, how many would you expect to have BP> 160? Give your answer to the nearest person. Note: I had a bit of an issue encoding rounded answers, so try rounding both up and down if there's an issue! ____  people

c. Stage 1 high BP is specified as systolic BP between 140 and 160. What percentage of adults in the US qualify for stage 1? _______ %

d. Your doctor tells you you are in the 30th percentile for blood pressure among US adults. What is your systolic BP? Round to 2 decimal places. ________ lbs

Part 2

In the country of United States of Heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 55.2 inches, and standard deviation of 8.7 inches.

What is the probability that the height of a randomly chosen child is between 44.35 and 45.05 inches? Do not round until you get your final answer, and then round to 3 decimal places.

Part 3

A distribution of values is normal with a mean of 130.7 and a standard deviation of 89.2.

Find the probability that a randomly selected value is greater than 202.1.
P(X > 202.1) =

Part 4

A distribution of values is normal with a mean of 150.1 and a standard deviation of 78.5.

Find the probability that a randomly selected value is between -38.3 and -30.5.
P(-38.3 < X < -30.5) =

Part 5

Company XYZ know that replacement times for the portable MP3 players it produces are normally distributed with a mean of 3.6 years and a standard deviation of 1.1 years.

Find the probability that a randomly selected portable MP3 player will have a replacement time less than 0.5 years?
P(X < 0.5 years) = ________

Enter your answer accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

If the company wants to provide a warranty so that only 4.4% of the portable MP3 players will be replaced before the warranty expires, what is the time length of the warranty?
warranty = _______ years

Part 6

The combined SAT scores for the students at a local high school are normally distributed with a mean of 1503 and a standard deviation of 308. The local college includes a minimum score of 1626 in its admission requirements.

What percentage of students from this school earn scores that fail to satisfy the admission requirement?
P(X < 1626) = _______%

On April 1, 1992, New Jersey’s minimum wage was increased from $4.25 to $5.05 per hour, while the minimum wage in Pennsylvania stayed at $4.25 per hour. Energetic students collected data on 410 fast food restaurants in New Jersey (the treatment group) and eastern Pennsylvania (the control group). The “before” period is February 1992, and the “after” period is November 1992. Using these data, we will estimate the effect of the “treatment,” raising the New Jersey minimum wage on employment at fast food restaurants in New Jersey (i.e., H_0:δ=0 versus H_A:δ<0). It is easier and more general to use the regression format to compute the differences-in-differences estimate using sample means. Let y=FTE employment , the treatment variable is the indicator variable NJ=1 if observation is from New Jersey, and zero if from Pennsylvania. The time indicator is D=1 if the observation is from November and zero if it is from February.

(a.)Write out the regression equation.

(b)Report the least squares estimates .

(c)At the α=.05 level of significance the regression region for the left tail test in above hypotheses is t≤-1.645, what is your conclusion?

(d)As with randomized control (quasi) experiments it is interesting to see the robustness of the result from (c). Please, add indicator variables for fast food chain and whether the restaurant was company-owned rather than franchise-owned. These changes alter the DID estimator?

(e)Please, add indicator variables for geographical regions within the survey area. These changes alter the DID estimator?

Describe the kind of data that are collected for an independent-measures t test and the hypotheses that the test evaluates. The key to helping formulate your explanation would be to include the assumptions of this statistical model, the type of sample used in this model, and a statement about the null hypothesis.

2. Suppose that the probability that a grant proposal is awarded by a funding agency is 0.3. (a) If, for a particular year, there are 100 proposals submitted to that agency, what is the probability that at most 20 proposals are awarded? Consider any necessary approximation.

The distribution of weights for 12 month old baby boys in the US is approximately normal with mean 22.5 pounds and a standard deviation of 2.2 pounds. a. if a 12 month old boy weights 20.3 pounds, what weight percentile is he in approximately. b. if a 12 month old boy is in the 84th percentile in weight, estimate his weight. c. Estimate the weight of a 12 month old boy who is in the 25th percentile by weight. d. Estimate the weight of a 12 month old boy who is in the 75 percentile by weight.

A quality characteristic X follows a Normal distribution with mean 100 and standard deviation 2 when the production process is in control.  

Part (a): Suppose that the lower and upper specification limits are 94 and 106, respectively.  What is the percentage of produced product items that are non-conforming, i.e., do not conform to the specification limits, when the process is indeed in control?

Part (b): The management has decided to monitor the process with and R control charts with a sample size of 4.  What should be the lower limit, centerline and the upper limit for each of the two control charts?

1. (18.10) Emissions of sulfur dioxide by industry set off chemical changes in the atmosphere that result in "acid rain." The acidity of liquids is measured by pH on a scale of 0 to 14. Distilled water has pH 7.0, and lower pH values indicate acidity. Normal rain is somewhat acidic, so acid rain is sometimes defined as rainfall with a pH below 5.0. Suppose that pH measurements of rainfall on different days in a Canadian forest follow a Normal distribution with standard deviationσ= 0.5. A sample ofndays finds that the mean pH isx= 4.8.

Give a 80 % confidence interval for the mean pH μ when n = 5, n = 15, and n = 40

n= 5 ____to ____

n= 15__ to ___

n= 40 __ to __

Recall that Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Now suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 216 numerical entries from the file and r = 52 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1.

(i) Test the claim that p is less than 0.301. Use α = 0.10.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: p = 0.301; H₁: p < 0.301

H₀: p = 0.301; H₁: p ≠ 0.301    

H₀: p < 0.301; H₁: p = 0.301

H₀: p = 0.301; H₁: p > 0.301

(b) What sampling distribution will you use?

The Student's t, since np < 5 and nq < 5.

The standard normal, since np > 5 and nq > 5.    

The Student's t, since np > 5 and nq > 5.

The standard normal, since np < 5 and nq < 5.

What is the value of the sample test statistic? (Round your answer to two decimal places.)


(c) Find the P-value of the test statistic. (Round your answer to four decimal places.)


Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.10 level, we reject the null hypothesis and conclude the data are statistically significant.

At the α = 0.10 level, we reject the null hypothesis and conclude the data are not statistically significant.    

At the α = 0.10 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
At the α = 0.10 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) Interpret your conclusion in the context of the application.

There is sufficient evidence at the 0.10 level to conclude that the true proportion of numbers with a leading 1 in the revenue file is less than 0.301.

There is insufficient evidence at the 0.10 level to conclude that the true proportion of numbers with a leading 1 in the revenue file is less than 0.301.    

(ii) If p is in fact less than 0.301, would it make you suspect that there are not enough numbers in the data file with leading 1's? Could this indicate that the books have been "cooked" by "pumping up" or inflating the numbers? Comment from the viewpoint of a stockholder. Comment from the perspective of the Federal Bureau of Investigation as it looks for money laundering in the form of false profits.

No. The revenue data file seems to include more numbers with higher first nonzero digits than Benford's law predicts.

No. The revenue data file does not seem to include more numbers with higher first nonzero digits than Benford's law predicts.   

Yes. The revenue data file seems to include more numbers with higher first nonzero digits than Benford's law predicts.

Yes. The revenue data file does not seem to include more numbers with higher first nonzero digits than Benford's law predicts.

(iii) Comment on the following statement: If we reject the null hypothesis at level of significance α, we have not proved H_o to be false. We can say that the probability is α that we made a mistake in rejecting H_o. Based on the outcome of the test, would you recommend further investigation before accusing the company of fraud?

We have not proved H₀ to be false. Because our data lead us to reject the null hypothesis, more investigation is merited.

We have proved H₀ to be false. Because our data lead us to reject the null hypothesis, more investigation is not merited.    

We have not proved H₀ to be false. Because our data lead us to reject the null hypothesis, more investigation is not merited.

We have not proved H₀ to be false. Because our data lead us to accept the null hypothesis, more investigation is not merited.

The following relative frequency distribution was constructed from a population of 550. Calculate the population mean, the population variance, and the population standard deviation. (Negative values should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answers to 2 decimal places.)

Question 12 Unsaved A sample of University of Colorado students each viewed one of two simulated news reports about a terrorist bombing against the United States by a fictitious country. One report showed the bombing attack on a military target and the other on a cultural/educational site. Additionally, before viewing the news report, each student read one of two "primes." The first was a prime for forgiveness based on the biblical saying "Love thy enemy," while the second was a retaliatory prime based on the biblical saying "An eye for an eye, and a tooth for a tooth." After viewing the news report, the students were asked to rate on a scale of 1 to 12 what the U.S. reaction should be, with the lowest score (1) corresponding to the United States sending a special ambassador to the country and the highest score (12) corresponding to an all-out nuclear attack against the country.6 (Use a diagram like Figure 9.2 from the text to display the factors and treatments.) Identify the following in this experiment:

_____ eye-for-an-eye prime

_____ the students

_____ love thy neighbor prime

_____ rating of U.S. reaction to attack

_____ prime used

_____ cultural/educational target

_____ military target

_____ type of attack

Options:

1. Subjects

2. Factors

3. Treatments for the prime

4. Treatments for the type of attack

5. Response variable

Exercise 8-31 Algo The monthly closing stock prices (rounded to the nearest dollar) for Panera Bread Co. for the first six months of 2010 are reported in the following table. [You may find it useful to reference the t table.] Months Closing Stock Price January 145 February 144 March 149 April 146 May 150 June 140 Source: http://finance.yahoo.com.

a. Calculate the sample mean and the sample standard deviation. (Round intermediate calculations to at least 4 decimal places and "Sample mean" and "Sample standard deviation" to 2 decimal places.)

b. Calculate the 90% confidence interval for the mean stock price of Panera Bread Co., assuming that the stock price is normally distributed. (Round "t" value to 3 decimal places and final answers to 2 decimal places.)

Consider the following regression output with Sunday circulation of newspapers as dependent variable and Daily circulation as independent variable. Both Sunday and Daily circulation and measured in thousands of copies.

Given the output above choose whether the following statement is TRUE or FALSE.

Question 1
This regression is bad because we are only 39.8% confident that the intercept coefficient is not 0.

1. Quinnipiac University conducted a telephone survey with a randomly selected national sample of 1155 registered voters. The survey asked the respondents, “In general, how satisfied are you with the way things are going in the nation today?” (Quinnipiac University, February 7, 2017). Response categories were Very satisfied, Somewhat satisfied, Somewhat dissatisfied, Very dissatisfied, Unsure/No answer. a. What is the relevant population? b. What is the variable of interest? Is it qualitative or quantitative? c. What is the sample and sample size? d. What is the inference of interest to Gallup; that is, what are they trying to measure or learn about? e. What method of data collection is employed? f. How likely is the sample to be representative? g. Would it make more sense to use averages or percentages as a summary of the data for this question? h. Of the respondents, 24% said they felt somewhat satisfied. How many individuals provided this response?

find the sample size needed to give a margin of error to estimate a proportion within plus minus 2% within 99% confidence within 95% confidence within 90% confidence assume no prior knowledge about the population proportion p

Use R to complete the following questions. You should include your R code, output and plots in your answer.

1. Two methods of generating a standard normal random variable are:

a. Take the sum of 5 uniform (0,1) random numbers and scale to have mean 0 and standard deviation 1. (Use the properties of the uniform distribution to determine the required transformation).

b. Generate a standard uniform and then apply inverse cdf function to obtain a normal random variate (Hint: use qnorm).

For each method generate 10,000 random numbers and check the distribution using

a. Normal probability plot

b. Mean and standard deviation

c. The proportion of the data lying within the theoretical 2.5 and 97.5 percentiles and the 0.5 and 99.5 percentiles. (Hint: The ifelse function will be useful)