Data for 64 female college athletes was collected. The data on weight​ (in pounds) are roughly bell shaped with x overbar equals 132x=132 and s equals 13s=13. Complete parts a and b below.

a. Give an interval within which about 68​% of the weights fall.

#2. Listed below are the amounts of net worth​ (in millions of​dollars) of the ten wealthiest celebrities in a country. Construct a 90​% confidence interval. What does the result tell us about the population of all​ celebrities? Do the data appear to be from a normally distributed population as​ required? 264 217 191 162 161 152 150 150 150 145 What is the confidence interval estimate of the population mean u ? ​

$------million<μ< $-------million (Round to one decimal place as​ needed.)

What does the result tell us about the population of all ​celebrities? Select the correct choice below​ and, if​ necessary, fill in the answer​box(es) to complete your choice. We are confident that 90​% of all celebrities have a net worth between $------million<μ< $-------million (Round to one decimal place as​ needed.)

We are 90​% confident that the interval from $------million<μ< $------- actually contains the true mean net worth of all celebrities. ​(Round to one decimal place as​needed.)

Because the ten wealthiest celebrities are not a representative​ sample, this​ doesn't provide any information about the population of all celebrities. Do the data appear to be from a normally distributed population as​ required?

A. ​Yes, but the points in the normal quantile plot do not lie reasonably close to a straight line or show a systematic pattern that is a straight line pattern.

B. ​Yes, because the pattern of the points in the normal quantile plot is reasonably close to a straight line.

C. ​No, because the points lie reasonably close to a straight​ line, but there is a systematic pattern that is not a straight line pattern.

D. ​No, but the points in the normal quantile plot lie reasonably close to a straight line and show some systematic pattern that is a straight line pattern.

#3. The pulse rates of 166 randomly selected adult males vary from a low of 35 bpm to a high of 107 bpm. Find the minimum sample size required to estimate the mean pulse rate of adult males. Assume that we want 98 % confidence that the sample mean is within 3 bpm of the population mean.

Find the sample size using the range rule of thumb to estimate q. N= ------ type whole number

B. assume that 10.7 bpm, based on values s= 10.7 bpm from the sample of 166 male pulse tares N= ------ type whole number

Compare the results from parts (a) and (b) which result is likely to be better?

The results from (a) is ----------- the results from part (b). The results from-------is likely to be better because ---------

#4. The Salaries of 45 college graduates who took a statistics course in college have a mean, x, of $ 64,900 . Assuming a standard deviation, q, of $19,881 , construct a 95 % confidence interval for estimating the population mean u. $ -----<μ< $------ round to nearest integer as needed

A kayak race is held each August on the South Arm of Lake Charlevoix, Charlevoix County, Michigan. The "course" starts at the public launch in East Jordan, MI and ends at the DNR launch at Dutchman's Bay, a distance of approximately two nautical miles. Participants are individual paddlers in identical Old Town sit inside Sorrento 106sk kayaks. The organizer wants to investigate if there is a relationship between the amount of experience (three categories) and minutes to complete the course. She wants to control for age. She also wants suggestions about other data that might be collected to find additional relationships (e.g. water temperature).

The data from a random sample from a recent year's event is provided below:

KAYAK RACE DATA SET

Experience

1 = participation in 10 or more kayak events

2 = participation in 4 to 9 kayak events

3 = participation in 3 kayak events

Complete the following:

Import / post the data above to create an SPSS data file (sav)

Conduct an ANCOVA analysis

Respond to the organizers current research question

Propose two future data categories (not including example above of water temperature) and rationale for each.

Rocky Mountain National Park is a popular park for outdoor recreation activities in Colorado. According to U.S. National Park Service statistics, 46.7% of visitors to Rocky Mountain National Park in 2018 entered through the Beaver Meadows park entrance, 24.3% of visitors entered through the Fall River park entrance, 6.3% of visitors entered through the Grand Lake park entrance, and 22.7% of visitors had no recorded point of entry to the park.† Consider a random sample of 175 Rocky Mountain National Park visitors. Use the normal approximation of the binomial distribution to answer the following questions. (Round your answers to four decimal places.)

(a)

What is the probability that at least 85 visitors had a recorded entry through the Beaver Meadows park entrance?

(b)

What is the probability that at least 80 but less than 90 visitors had a recorded entry through the Beaver Meadows park entrance?

(c)

What is the probability that fewer than 11 visitors had a recorded entry through the Grand Lake park entrance?

(d)

What is the probability that more than 40 visitors have no recorded point of entry?

Make an example of a binomial experiment and its binomial random variable X (Do not use a coin-flipping example, anything else is fine)

1. What is your trial? How many trials (which is n) do you have? Why do you think they are independent which is one of the required conditions for the binomial experiments?
2. Which outcome of your trial is considered a success?
3. The probability of having a success per trial, P. Give the probability value of P. If you are using an experimental (relative frequency) probability, use hypothetical numbers to derive the value of P.
4. You have n trials. How does P (X=1) differ from " the probability of having a success per trial, P" ? Explain.

The prices of condos in a city are normally distributed with a mean of $100,000 and a standard deviation of $32,000.

Answer the following questions rounding your solutions to 4 decimal places.

1. The city government exempts the cheapest 6% of the condos from city taxes. What is the maximum price of the condos that will be exempt from city taxes?

2. If 2% of the most expensive condos are subject to a luxury tax, what is the minimum price of condos that will be subject to the luxury tax?

A professor at a local university noted that the grades of her students were normally distributed with a mean of 73 and a standard deviation of 11.

Answer the following questions rounding your solutions to 4 decimal places.

1. The professor has informed the class that 7.93 percent of her students received grades of A. What is the minimum score needed to receive a grade of A?

2. Students who made 57.93 or lower on the exam failed the course. What fraction of students failed the course?

3. If 69.5 percent of the students received grades of C or better, what is the minimum score of those who received C's?

A researcher conducts a study on the effects of amount of sleep on creativity. The creativity scores for four levels of sleep (2 hours, 4 hours, 6 hours, and 8 hours) are presented below:

            2 Hours of Sleep         4 Hours of Sleep         6 Hours of Sleep         8 Hours of Sleep

                        3                                  4                                  10                                10

                        5                                  7                                  11                                13

                        6                                  8                                  13                                10

                        4                                  3                                  9                                9

                        2                                  2                                  10                                10

Pretend that you have only the 4-hour group of data and the 6-hour group of data. Also pretend that this data set does not meet all the conditions for parametric testing. Without using a parametric procedure, compare the two samples (4-hour and 6-hour samples) and test for a significant (p < 0.05) difference.

(a) What is the appropriate null hypothesis for this situation? What is the alternative hypothesis?

(b)Identify and perform the most appropriate procedure to test the null hypothesis, present your

      results, and draw your conclusion using a complete sentence.

A coin is tossed 6 times. Let X be the number of Heads in the resulting combination. Calculate the second moment of X.

(A).Calculate the second moment of X

(B). Find Var(X)

This assignment is designed to illustrate how a spreadsheet program such as Microsoft Excel supplemented by PHStat can enable you to easily accomplish hypothesis tests and confidence intervals that compare two population parameters. All work should be accomplished using PHStat. You should provide all the appropriate printouts of the tests you do and the confidence intervals you create along with explanations of the meaning of your answers and business implications for each problem. The assignment should be submitted to the drop box created for this purpose. Use the information in your text both within the chapter and at the end of the chapter and in the appendices at the end of the book as a guide to completing the assignment of needed.

You have been asked once again to study the mean tuition at private universities throughout the United States. You will also again study the proportions of universities throughout the United States that regularly award more than 50% of their students some form of financial aid. The specific questions you will be asked to answer are stated below. In addition, appropriate sample data for the studies you will be accomplishing is given below. Answer the following questions concerning the situations posed.

You first wish to know whether there is a difference in the mean tuition at private universities that are located east and west of the Mississippi River. The population standard deviation in the tuition of private universities east of the Mississippi is thought to equal $11,000, and the standard deviation in the tuition of private universities west of the Mississippi is thought to equal $10,000. A random sample of 25 private universities located east of the Mississippi River is chosen. The sample mean tuition for these universities is found to equal $19,850. A random sample of 35 universities located west of the Mississippi River is selected. The sample mean tuition for these universities is found to equal $14,765. At each of the 5% and 10% levels of significance, is there a difference in the mean tuition rates for these two groups of private universities? If at either level of significance, you do observe that there is a difference in the mean tuition, is that difference different from $2,000? If the software permits it, construct both 95% and 90% confidence intervals for the difference in the mean tuition for universities located east and west of the Mississippi River. Explain their meanings in the context of the problem. Use these intervals to test whether there is a difference in the mean tuition rates. Use the 95%

confidence interval to perform the test at the 5% level of significance and the 90% confidence interval to perform the test at the 10% level of significance.

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 207.2-cm and a standard deviation of 2.3-cm. For shipment, 17 steel rods are bundled together. Round all answers to four decimal places if necessary.

What is the distribution of XX? XX ~ N(,)

What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)

For a single randomly selected steel rod, find the probability that the length is between 207.4-cm and 207.9-cm.

For a bundled of 17 rods, find the probability that the average length is between 207.4-cm and 207.9-cm.

For part d), is the assumption of normal necessary? YesNo

LicensePoints possible: 1

please work on this assignment

Twenty-five percent of the customers entering a grocery store between 5 P.M. and 7 P.M. use an express checkout. Consider five randomly selected customers, and let x denote the number among the five who use the express checkout.

(a) What is p(3), that is, P(x = 3)? (Round the answer to five decimal places.)
p(3) =

(b) What is P(x ≤ 1)? (Round the answer to five decimal places.)
P(x ≤ 1) =

(c) What is P(2 ≤ x)? (Round the answer to five decimal places. Hint: Make use of your computation in Part (b).)
P(2 ≤ x) =

(d) What is P(x ≠ 3)? (Round the answer to five decimal places.)
P(x ≠ 3) =

R code to obtain the goodness of fit G^2, its p-value, and its AIC value given a dataset?

3) Estimate a regression line Y = intercept + slope X. What are the intercept and the slope? Write the equation of the line you estimated.

4) Discuss the regression results. What does the slope mean?

5) What is the correlation coefficient equal to?

6) Do a hypothesis test in which the null hypothesis is that the correlation coefficient is equal to zero agains the alternative that it is different from zero. What is the test statistic? What is the p-value? What is your conclusion?

Suppose a MTH instructor is teaching two sections of the course, and administers an exam. The instructor grades the exams, and calculates the mean exam score to be 65 for section 1 and 83 for section 2.

a- Do you (not the instructor) have enough information to calculate the overall mean for all students enrolled on either section? Explain

b- Suppose section 1 has 35 students and section 2 has 25 students. Calculate the overall mean. Is the overall mean closer to 65 or to 83?

c- Give an example of two section sizes n1 and n2 for which the overall mean is more than 81 (show your calculation)

Professor Fair believes that extra time does not improve grades on exams. He randomly divided a group of 300 students into two groups and gave them all the same test. One group had exactly 1 hour in which to finish the test, and the other group could stay as long as desired. The results are shown in the following table. Test at the 0.01 level of significance that time to complete a test and test results are independent. Time A B C F Row Total 1 h 23 41 56 15 135 Unlimited 18 47 80 20 165 Column Total 41 88 136 35 300 (i) Give the value of the level of significance. State the null and alternate hypotheses. H0: Time to take a test and test score are independent. H1: Time to take a test and test score are not independent. H0: The distributions for a timed test and an unlimited test are different. H1: The distributions for a timed test and an unlimited test are the same. H0: The distributions for a timed test and an unlimited test are the same. H1: The distributions for a timed test and an unlimited test are different. H0: Time to take a test and test score are not independent. H1: Time to take a test and test score are independent. (ii) Find the sample test statistic. (Round your answer to two decimal places.) (iii) Find or estimate the P-value of the sample test statistic. P-value > 0.100 0.050 < P-value < 0.100 0.025 < P-value < 0.050 0.010 < P-value < 0.025 0.005 < P-value < 0.010 P-value < 0.005 (iv) Conclude the test. Since the P-value is ≥ α, we do not reject the null hypothesis. Since the P-value < α, we do not reject the null hypothesis. Since the P-value < α, we reject the null hypothesis. Since the P-value ≥ α, we reject the null hypothesis. (v) Interpret the conclusion in the context of the application. At the 1% level of significance, there is insufficient evidence to claim that time to do a test and test results are not independent. At the 1% level of significance, there is sufficient evidence to claim that time to do a test and test results are not independent.