1. It is believed that nearsightedness affects about 8% of all children. In a random sample of 194 children, 21 are nearsighted.
(a) Construct hypotheses appropriate for the following question: do these data provide evidence that the 8% value is inaccurate?

• Ho: p = .08
  Ha: p ≠ .08
• Ho: p = .08
  Ha: p < .08
• Ho: p = .08
  Ha: p > .08

(b) What proportion of children in this sample are nearsighted?
(round to four decimal places)
(c) Given that the standard error of the sample proportion is 0.0195 and the point estimate follows a nearly normal distribution, calculate the test statistic (use the Z-statistic).
Z =  (please round to two decimal places)
(d) What is the p-value for this hypothesis test?
p =  (please round to four decimal places)
(e) What is the conclusion of the hypothesis test?

• Since p ≥ α we do not have enough evidence to reject the null hypothesis
• Since p<α we reject the null hypothesis and accept the alternative
• Since p<α we fail to reject the null hypothesis
• Since p ≥ α we accept the null hypothesis

2. Test the claim that the mean GPA of night students is larger than 2.7 at the 0.005 significance level.

(1)The null and alternative hypothesis would be:

a) H0:p≥0.675
H1:p<0.675   

b) H0:p=0.675
H1:p≠0.675

c) H0:μ≤2.7   
H1:μ>2.7

d) H0:p≤0.675   
H1:p>0.675   

e) H0:μ=2.7
H1:μ≠2.7

f) H0:μ≥2.7
H1:μ<2.7

(2) The test is:

-two-tailed

-left-tailed

-right-tailed

(3) Based on a sample of 35 people, the sample mean GPA was 2.73 with a standard deviation of 0.04

The p-value is: ____ (to 2 decimals)

Based on this we:

• Reject the null hypothesis
• Fail to reject the null hypothesis

Use simulation in SAS.

FICO scores nationally have an average of 640 with a standard deviation of 60. If you simulated the credit scores of 10,000 borrowers, what percent of FICO scores are less than 500? Greater than 850? Find the mean and standard deviation of scores that meet these conditions.

How can you demonstrate that the probability of X successes in a binomial distribution is given by P(X=x)=nCx p^x q^(n-x)

In the Southern Ocean food web, the krill species Euphausia superba is the most important prey species for many marine predators, from seabirds to the largest whales. Body lengths of the species are normally distributed with a mean of 40 mm and a standard deviation of 12 mm. (a) What is the probability that a randomly selected krill is longer than 46 mm? (b) Describe the distribution of the mean length of a sample of four krill. (c) What is the probability that the mean length of a sample of four krill is more than 46 mm? (d) Could you estimate the probabilities from parts (a) and (c) if the lengths of krill had a skewed distribution?

Discuss recommendations for best practices in Structural Equation Modeling.

Visit the NASDAQ historical prices weblink. First, set the date range to be for exactly 1 year ending on the Monday that this course started. For example, if the current term started on April 1, 2018, then use April 1, 2017 – March 31, 2018. (Do NOT use these dates. Use the dates that match up with the current term.) Do this by clicking on the blue dates after “Time Period”. Next, click the “Apply” button. Next, click the link on the right side of the page that says “Download Data” to save the file to your computer.

This project will only use the Close values. Assume that the closing prices of the stock form a normally distributed data set. This means that you need to use Excel to find the mean and standard deviation. Then, use those numbers and the methods you learned in sections 6.1-6.3 of the course textbook for normal distributions to answer the questions. Do NOT count the number of data points.

Complete this portion of the assignment within a single Excel file. Show your work or explain how you obtained each of your answers. Answers with no work and no explanation will receive no credit.

1. a) Submit a copy of your dataset along with a file that contains your answers to all of the following questions.

b) What the mean and Standard Deviation (SD) of the Close column in your data set?

c) If a person bought 1 share of Google stock within the last year, what is the probability that the stock on that day closed at less than the mean for that year? Hint: You do not want to calculate the mean to answer this one. The probability would be the same for any normal distribution. (5 points)

2. If a person bought 1 share of Google stock within the last year, what is the probability that the stock on that day closed at more than $950? (5 points)
3. If a person bought 1 share of Google stock within the last year, what is the probability that the stock on that day closed within $50 of the mean for that year? (between 50 below and 50 above the mean) (5 points)
4. If a person bought 1 share of Google stock within the last year, what is the probability that the stock on that day closed at less than $800 per share. Would this be considered unusal? Use the definition of unusual from the course textbook that is measured as a number of standard deviations (5 points)
5. At what prices would Google have to close in order for it to be considered statistically unusual? You will have a low and high value. Use the definition of unusual from the course textbook that is measured as a number of standard deviations. (5 points)
6. What are Quartile 1, Quartile 2, and Quartile 3 in this data set? Use Excel to find these values. This is the only question that you must answer without using anything about the normal distribution. (5 points)
7. Is the normality assumption that was made at the beginning valid? Why or why not? Hint: Does this distribution have the properties of a normal distribution as described in the course textbook? Real data sets are never perfect, however, it should be close. One option would be to construct a histogram like you did in Project 1 to see if it has the right shape. Something in the range of 10 to 12 classes is a good number. (5 points)

There are also 5 points for miscellaneous items like correct date range, correct mean, correct SD, etc.

Provided below are summary statistics for independent simple random samples from two​ normally-distributed populations. Conduct the required hypothesis test and obtain the specified confidence interval.

xbar=12, s1=2.4, n1=20, xbar2=11, s2=7, n2=15

a) Right-tailed test, a=0.05. Find the test statistic. Find the p-value

b) 90% confidence interval. Find the confidence interval

A chemist analyzes seawater samples for two heavy metals: lead and mercury. Past experience indicates that 38% of the samples taken from near the mouth of a river on which numerous industrial plants are located contain toxic levels of lead or mercury; 32% contain toxic levels of lead and 16% contain toxic levels of mercury

What is the probability that a randomly selected sample will not contain lead or will not contain mercury?

An experiment on memory was performed, in which 16 subjects were randomly assigned to one of two groups, called "Sentences" or "Intentional". Each subject was given a list of 50 words. Subjects in the "Sentences" group were told to form multiple sentences, each using at least two words from the list, and to keep forming sentences until all the words were used at least once. Subjects in the "Intentional" group were told to spend five minutes memorizing as many of the 50 words as possible. Subjects from both groups were then asked to write down as many words from their lists as they could recall. The data are in the table below.

Enter this data into JMP in "long form" (e.g. each column should be a variable and each row should be an observation).
IMPORTANT: to format this data correctly, you need to think about what your two variables are (they are not 'Sentences' and 'Intentional'). You may want to look at how the deflategate data are formatted if you have trouble figuring this out.

We are interested in determining if there is a significant difference in the average number of words recalled for subjects in the "sentences" group vs. subjects in the "intentional" group, using α = 0.05. Use JMP to answer the questions below, and round all answers to three decimal places.

a. The appropriate null/alternative hypothesis pair for this study is:
(you have two attempts at this question)

H₀: μ_sentences - μ_intentional = 0 ; H_A: μ_sentences - μ_intentional > 0Ho: μ_sentences - μ_intentional = 0 ; H_A: μ_sentences - μ_intentional < 0    H₀: μ_sentences - μ_intentional = 0 ; H_A: μ_sentences - μ_intentional ≠ 0H₀: μ_d = 0 ; H_A: μ_d < 0H₀: μ_d = 0 ; H_A: μ_d ≠ 0H₀: μ_d = 0 ; H_A: μ_d > 0

b. Enter the values for the following statistics:

x_sentences =  
s_sentences =  
x_intentional =  
s_intentional =  
(x_sentences - x_intentional) =  
standard error of (x_sentences - x_intentional) =  (you have to use 'Analyze / Fit Y by X' to get JMP to calculate this)
test statistic: t =  
p-value =  

c. Report the 95% confidence interval JMP gives for μ_sentences - μ_intentional

Lower bound =  
Upper bound =  

d. From these results, our statistical conclusion should be:
(You have two attempts at this question.)

The means for "sentences" and "intentional" differ significantly, because the p-value is less than α and zero is inside the confidence intervalThe means for "sentences" and "intentional" differ significantly, because the p-value is less than α and zero is outside the confidence interval    The means for "sentences" and "intentional" differ significantly, because the p-value is less than α and -4 is inside the confidence intervalThe means for "sentences" and "intentional" differ significantly, because the p-value is less than α and -4 is outside the confidence intervalThe means for "sentences" and "intentional" do not differ significantly, because the p-value is greater than α and zero is inside the confidence intervalThe means for "sentences" and "intentional" do not differ significantly, because the p-value is greater than α and zero is outside the confidence intervalThe means for "sentences" and "intentional" do not differ significantly, because the p-value is greater than α and -4 is inside the confidence intervalThe means for "sentences" and "intentional" do not differ significantly, because the p-value is greater than α and -4 is outside the confidence interval

A family consisting of four persons—A, B, C, and D—belongs to a medical clinic that always has a doctor at each of stations 1, 2, and 3. During a certain week, each member of the family visits the clinic once and is assigned at random to a station. The experiment consists of recording the station number for each member. Suppose that any incoming individual is equally likely to be assigned to any of the three stations irrespective of where other individuals have been assigned.

(a) What is the probability that all four family members are assigned to the same station?


(b) What is the probability that at most three family members are assigned to the same station?


(c) What is the probability that one station has two family members at it and the others have only one?

You perform 1000 significance tests using a = 0.05. Assuming that all null hypotheses are true, about how many of the test results would you expect to be statistically significant? Explain how you obtained your answer.

You work for a pharmaceutical company wanting to make a new flavor of cough syrup. You are asked to conduct research on flavor preferences. You would like to know whether people like Cherry Lime, Vanilla Mint and Cinnamon Mocha flavors differently. You divided all potential customers into geological regions and randomly selected a few regions to recruit your study participants from. Then from the selected regions, your randomly recruited 24 participants, which is representative of all potential customers of your cough syrup. You asked those 24 participants to choose their favorite flavor from the three. 13 of them choose Cherry Lime, 4 of them chose Vanilla Mint, and 7 of them choose Cinnamon Mocha.

Please answer the following.

What is the study sample?

What is the target population?

What is the sampling method?

what is the measurment scale?

What type of transformation can be used with this data?

Give an example of how you can transform the code of this data?

Mean, meadian, and mode?

Researchers equipped random samples of 46 male and 58 female students from a large university with a small device that secretly records sound for a random 30 seconds during each 12.5-minute period over two days. Then they counted the number of words spoken by each subject during each recording period and, from this, estimated how many words per day each subject speaks. The female estimates had a mean of 16,177 words per day with a standard deviation of 7520 words per day. For the male estimates, the mean was 16,569 and the standard deviation was 9108. Do these data provide convincing evidence of a difference in the average number of words spoken in a day by male and female students at this university?

a) What is the critical value for this test?

b) What is the p-value for this test?

c) What is the test statistic for this test?

d) What is the decision for this test?

At a certain coffee​ shop, all the customers buy a cup of coffee and some also buy a doughnut. The shop owner believes that the number of cups he sells each day is normally distributed with a mean of 340 cups and a standard deviation of 18 cups. He also believes that the number of doughnuts he sells each day is independent of the coffee sales and is normally distributed with a mean of 180 doughnuts and a standard deviation of 16.

a) The shop is open every day but Sunday. Assuming​ day-to-day sales are​ independent, what's the probability​ he'll sell over 2000 cups of coffee in a​ week?

__________________ ​(Round to three decimal places as​ needed.)

The daily exchange rates for the​ five-year period 2003 to 2008 between currency A and currency B are well modeled by a normal distribution with mean 1.798 in currency A​ (to currency​ B) and standard deviation 0.047 in currency A. Given this​ model, and using the​ 68-95-99.7 rule to approximate the probabilities rather than using technology to find the values more​ precisely, complete parts​ (a) through​ (d).

a) What would the cutoff rate be that would separate the highest 16​% of currency​ A/currency B​ rates?

The cutoff rate would be ______________

​(Type an integer or a decimal rounded to the nearest thousandth as​ needed.)

The daily exchange rates for the​ five-year period 2003 to 2008 between currency A and currency B are well modeled by a normal distribution with mean 1.425 in currency A​ (to currency​ B) and standard deviation 0.026 in currency A. Given this​ model, and using the​ 68-95-99.7 rule to approximate the probabilities rather than using technology to find the values more​ precisely, complete parts​ (a) through​ (d).

​a) What is the probability that on a randomly selected day during this​ period, a unit of currency B was worth less than 1.425 units of currency​ A?

The probability is _____________%

​(Type an integer or a​ decimal.)

The home run percentage is the number of home runs per 100 times at bat. A random sample of 43 professional baseball players gave the following data for home run percentages.

(a) Use a calculator with mean and standard deviation keys to find x and s. (Round your answers to two decimal places.)

(b) Compute a 90% confidence interval for the population mean μ of home run percentages for all professional baseball players. Hint: If you use the Student's t distribution table, be sure to use the closest d.f. that is smaller. (Round your answers to two decimal places.)

(c) Compute a 99% confidence interval for the population mean μ of home run percentages for all professional baseball players. (Round your answers to two decimal places.)