An exercise science major wants to try to use body weight to predict how much someone can bench press. He collects the data shown below on 30 male students. Both quantities are measured in pounds.

b) Compute a 95% confidence interval for the average bench press of 150 pound males. What is the lower limit? Give your answer to two decimal places.  

c) Compute a 95% confidence interval for the average bench press of 150 pound males. What is the upper limit? Give your answer to two decimal places.  

d) Compute a 95% prediction interval for the bench press of a 150 pound male. What is the lower limit? Give your answer to two decimal places.  

e) Compute a 95% prediction interval for the bench press of a 150 pound male. What is the upper limit? Give your answer to two decimal places.  

Thoroughly answer the following questions:

Why are adjustments needed in determining risks and rates?

In product design for human use and recommended guideline for the product’s human use, it is important to consider the weights of people so that airplanes or elevators aren’t overloaded. Based on data from the National Health Survey, the weight of adults in the United States has a mean of 181 pound (the average of 195.5 for males and 166.2 for females, assuming, arbitrarily, equal male and female population) with a standard deviation of 30 pounds. An airplane is designed to have a human carrying maximum-capacity 18,500 pounds. An Airline adopts the operation procedure of maximum passenger number (n), based on the concept of the probability of a randomly selected n passengers exceeding the maximum-capacity to be less than 0.01 (i.e., 1%). a) [3 pts] Determine n b) b) [2 pts] What will be the value of n if the probability of exceeding the maximum-capacity is no more than 0.001 (i.e., 0.1%)?

Now suppose Thermata officers want to ascertain employee satisfaction with the company. They randomly sample nine employees and ask them to complete a satisfaction survey under the supervision of an independent testing organisation. As part of this survey, employees are asked to respond to questions on a 5-point scale where 1 is low satisfaction and 5 is high satisfaction. The questions and the results of the survey are shown in the next column. Analyse the data by finding a confidence interval (with =0.05) to estimate the population response to each of these questions. Provide your interpretation and discussions of the results.

A local car dealer is attempting to determine which premium will draw the most visitors to its showroom. An individual who visits the showroom and takes a test ride is given a premium with no obligation. The dealer chose four premiums and offered each for one week. The results are as follows:

3(a): Please identify the research question (one sentence).

Here are some examples of the research question:

How/why A is related to B?

Does A cause/equal/bigger/smaller/explain than B?

Whether A is equal/bigger/smaller than B?

3(b) Please generate the appropriate hypothesis

H0:

Ha:

3(c): Find the appropriate statistical test, compute the test statistics. Please give detailed calculation procedures.

3(d): Based on your computed test statistics, draw your conclusions

The age distribution of the Canadian population and the age distribution of a random sample of 455 residents in the Indian community of a village are shown below.

Use a 5% level of significance to test the claim that the age distribution of the general Canadian population fits the age distribution of the residents of Red Lake Village.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: The distributions are different.
H₁: The distributions are the same.H₀: The distributions are the same.
H₁: The distributions are the same.    H₀: The distributions are different.
H₁: The distributions are different.H₀: The distributions are the same.
H₁: The distributions are different.

(b) Find the value of the chi-square statistic for the sample. (Round your answer to three decimal places.)


Are all the expected frequencies greater than 5?

YesNo    

What sampling distribution will you use?

uniformnormal    chi-squareStudent's tbinomial

What are the degrees of freedom?


(c) Estimate the P-value of the sample test statistic.

P-value > 0.1000.050 < P-value < 0.100    0.025 < P-value < 0.0500.010 < P-value < 0.0250.005 < P-value < 0.010P-value < 0.005

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis that the population fits the specified distribution of categories?

Since the P-value > α, we fail to reject the null hypothesis.Since the P-value > α, we reject the null hypothesis.    Since the P-value ≤ α, we reject the null hypothesis.Since the P-value ≤ α, we fail to reject the null hypothesis.

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

At the 5% level of significance, the evidence is insufficient to conclude that the village population does not fit the general Canadian population.At the 5% level of significance, the evidence is sufficient to conclude that the village population does not fit the general Canadian population.

The data below are the heights of fathers and sons (inches). There are 8 rows in total.

Father Son

1. Which statistical test would you use to determine if there is a tendency for tall fathers to have tall sons and short fathers to have short sons? Test for the statistical significance.

2. Compute the regression equation for predicting sons' heights from fathers' heights.

3. Use the equation from #2 to predict the height of a son whose father is 46 inches tall.

4. Should you use the regression equation to predict the hight of a son whose father had a height of 25" when he was the same age as his son?

5. Which statistical test would you use to determine if generations get taller. The question is, are sons taller than their fathers were at the same age?

You may need to use the appropriate appendix table or technology to answer this question.

Consider a multiple-choice examination with 50 questions. Each question has four possible answers. Assume that a student who has done the homework and attended lectures has a 65% chance of answering any question correctly. (Round your answers to two decimal places.)

(a)

A student must answer 44 or more questions correctly to obtain a grade of A. What percentage of the students who have done their homework and attended lectures will obtain a grade of A on this multiple-choice examination? Use the normal approximation of the binomial distribution to answer this question.

(b)

A student who answers 36 to 39 questions correctly will receive a grade of C. What percentage of students who have done their homework and attended lectures will obtain a grade of C on this multiple-choice examination? Use the normal approximation of the binomial distribution to answer this question.

(c)

A student must answer 30 or more questions correctly to pass the examination. What percentage of the students who have done their homework and attended lectures will pass the examination? Use the normal approximation of the binomial distribution to answer this question.

(d)

Assume that a student has not attended class and has not done the homework for the course. Furthermore, assume that the student will simply guess at the answer to each question. What is the probability that this student will answer 30 or more questions correctly and pass the examination? Use the normal approximation of the binomial distribution to answer this question.

Keeping water supplies clean requires regular measurement of levels of pollutants. The measurements are indirecta typical analysis involves forming a dye by a chemical reaction with the dissolved pollutant, then passing light through the solution and measuring its "absorbence." To calibrate such measurements, the laboratory measures known standard solutions and uses regression to relate absorbence and pollutant concentration. This is usually done every day. Here is one series of data on the absorbence for different levels of nitrates. Nitrates are measured in milligrams per liter of water. Nitrates 50 50 100 200 400 800 1200 1600 2000 2000 Absorbence 7.0 7.6 12.9 24.0 47.0 93.0 138.0 183.0 229.0 226.0 (a) Chemical theory says that these data should lie on a straight line and if the correlation is not at least 0.997 then the calibration procedure is repeated. Find the correlation. (Use 4 decimal places.) r = (b) Must the calibration be done again? Yes No (c) The calibration process sets nitrate level and measures absorbence. Once established, the linear relationship will be used to estimate the nitrate level in water from a measurement of absorbance. What is the equation of the line used for estimation? (Use 2 decimal places for intercept and 3 decimal places for slope.) y hat = + x (d) What is the estimated nitrate level in a water specimen with absorbence 41? (Use 1 decimal place.) mg/l (e) Do you expect estimates of nitrate level from absorbence to be quite accurate? Since the calibration is so important, it is inaccurate to use this regression to predict. This prediction should be very accurate because the relationship is so strong as indicated by r. This prediction should be very inaccurate because the relationship is too perfectly linear. This prediction is of a value that is not in the range of the data and therefore cannot be accurate.

The following data was reported on total Fe for four types of iron formation (1 = carbonate, 2 = silicate, 3 = magnetite, 4 = hematite). 1: 20.7 28.1 27.8 27.0 28.1 25.2 25.3 27.1 20.5 31.8 2: 26.4 24.0 26.2 20.2 24.2 34.0 17.1 26.8 23.7 24.5 3: 29.9 34.0 27.5 29.4 27.9 26.2 29.9 29.5 30.0 35.7 4: 37.1 44.2 34.1 30.3 31.8 33.1 34.1 32.9 36.3 25.8 Carry out an analysis of variance F test at significance level 0.01. State the appropriate hypotheses. H0: μ1 = μ2 = μ3 = μ4 Ha: all four μi's are unequal H0: μ1 ≠ μ2 ≠ μ3 ≠ μ4 Ha: at least two μi's are equal H0: μ1 ≠ μ2 ≠ μ3 ≠ μ4 Ha: all four μi's are equal H0: μ1 = μ2 = μ3 = μ4 Ha: at least two μi's are unequal Summarize the results in an ANOVA table. (Round your answers two decimal places.) Source df Sum of Squares Mean Squares f Treatments Error Total Give the test statistic. (Round your answer to two decimal places.) f = What can be said about the P-value for the test? P-value > 0.100 0.050 < P-value < 0.100 0.010 < P-value < 0.050 0.001 < P-value < 0.010 P-value < 0.001 State the conclusion in the problem context. Reject H0. There is sufficient evidence to conclude that the total Fe differs for at least two of the four formations. Reject H0. There is insufficient evidence to conclude that the total Fe differs for the four formations. Fail to reject H0. There is insufficient evidence to conclude that the total Fe differs for the four formations. Fail to reject H0. There is sufficient evidence to conclude that the total Fe differs for at least two of the four formations. You may need to use the appropriate table in the Appendix of Tables to answer this question.

When σ is unknown and the sample is of size n ≥ 30, there are two methods for computing confidence intervals for μ. (Notice that, When σ is unknown and the sample is of size n < 30, there is only one method for constructing a confidence interval for the mean by using the Student's t distribution with d.f. = n - 1.) Method 1: Use the Student's t distribution with d.f. = n - 1. This is the method used in the text. It is widely employed in statistical studies. Also, most statistical software packages use this method. Method 2: When n ≥ 30, use the sample standard deviation s as an estimate for σ, and then use the standard normal distribution. This method is based on the fact that for large samples, s is a fairly good approximation for σ. Also, for large n, the critical values for the Student's t distribution approach those of the standard normal distribution. Consider a random sample of size n = 30, with sample mean x = 45.2 and sample standard deviation s = 5.3.

(a) Compute 90%, 95%, and 99% confidence intervals for μ using Method 1 with a Student's t distribution. Round endpoints to two digits after the decimal.

90% Lower limit and Upper limit

95% Lower limit and Upper limit

99% Lower limit and Upper limit

(d) Now consider a sample size of 50. Compute 90%, 95%, and 99% confidence intervals for μ using Method 1 with a Student's t distribution. Round endpoints to two digits after the decimal.

90% Lower limit and Upper limit

95% Lower limit and Upper limit

99% Lower limit Upper limit

Please show me how to do this on a TI 84 Calculator if possible. Thank you!

The Normal Probability distribution has many practical uses. Please provide some examples of real life data sets that are normally distributed.

Researchers gave 40 index cards to a waitress at an Italian restaurant in New Jersey. Before delivering the bill to each customer, the waitress randomly selected a card and wrote on the bill the same message that was printed on the index card. Twenty of the cards had the message "The weather is supposed to be really good tomorrow. I hope you enjoy the day!" Another 20 cards contained the message "The weather is supposed to be not so good tomorrow. I hope you enjoy the day anyway!"

After the customers left, the waitress recorded the amount of the tip, percent of bill, before taxes. Given are the tips for those receiving the good‑weather message.

Given are the tips for the 20 customers who received the bad‑weather message.

Stemplots for both data sets are shown.

Neither stemplot suggests a strong skew or the presence of strong outliers. Because of this, t procedures are reasonable here.

Is there good evidence that the two different messages produce different percent tips?

Let μ1 be the mean tip percent when the forecast is good, and let μ2 be the mean tip percent when the forecast is bad. Select the correct hypotheses statements that we want to test.

H0:μ1=μ2 versus Ha:μ1>μ2

H0:μ1=μ2 versus Ha:μ1≠μ2

H0:μ1=μ2 versus Ha:μ1<μ2

H0:μ1≠μ2 versus Ha:μ1<μ2

What degrees of freedom (df) would you use in the conservative two‑sample t procedures to compare the percentage of tips when the forecast is good and bad? (Enter your answer as a whole number.)

df=

What is the two‑sample t test statistic (rounded to three decimal places)?

t=

Test whether there is good evidence that the two different messages produce different percent tips at α=0.1 . The null hypothesis of no difference in tips due to the weather "forecast" is

not rejected.

rejected.

The following data represent crime rates per 1000 population for a random sample of 46 Denver neighborhoods.†

(a) Use a calculator with mean and sample standard deviation keys to find the sample mean x and sample standard deviation s. (Round your answers to one decimal place.)

(b) Let us say the preceding data are representative of the population crime rates in Denver neighborhoods. Compute an 80% confidence interval for μ, the population mean crime rate for all Denver neighborhoods. (Round your answers to one decimal place.)

(c) Suppose you are advising the police department about police patrol assignments. One neighborhood has a crime rate of 61 crimes per 1000 population. Do you think that this rate is below the average population crime rate and that fewer patrols could safely be assigned to this neighborhood? Use the confidence interval to justify your answer.

Yes. The confidence interval indicates that this crime rate is below the average population crime rate.

Yes. The confidence interval indicates that this crime rate does not differ from the average population crime rate.     

No. The confidence interval indicates that this crime rate is below the average population crime rate.

No. The confidence interval indicates that this crime rate does not differ from the average population crime rate.

(d) Another neighborhood has a crime rate of 75 crimes per 1000 population. Does this crime rate seem to be higher than the population average? Would you recommend assigning more patrols to this neighborhood? Use the confidence interval to justify your answer.

Yes. The confidence interval indicates that this crime rate does not differ from the average population crime rate.

Yes. The confidence interval indicates that this crime rate is higher than the average population crime rate.     

No. The confidence interval indicates that this crime rate is higher than the average population crime rate.

No. The confidence interval indicates that this crime rate does not differ from the average population crime rate.

(e) Compute a 95% confidence interval for μ, the population mean crime rate for all Denver neighborhoods. (Round your answers to one decimal place.)

(f) Suppose you are advising the police department about police patrol assignments. One neighborhood has a crime rate of 61 crimes per 1000 population. Do you think that this rate is below the average population crime rate and that fewer patrols could safely be assigned to this neighborhood? Use the confidence interval to justify your answer.

Yes. The confidence interval indicates that this crime rate is below the average population crime rate.

Yes. The confidence interval indicates that this crime rate does not differ from the average population crime rate.   

No. The confidence interval indicates that this crime rate is below the average population crime rate.

No. The confidence interval indicates that this crime rate does not differ from the average population crime rate.

(g) Another neighborhood has a crime rate of 75 crimes per 1000 population. Does this crime rate seem to be higher than the population average? Would you recommend assigning more patrols to this neighborhood? Use the confidence interval to justify your answer.

Yes. The confidence interval indicates that this crime rate does not differ from the average population crime rate.

Yes. The confidence interval indicates that this crime rate is higher than the average population crime rate.     

No. The confidence interval indicates that this crime rate is higher than the average population crime rate.

No. The confidence interval indicates that this crime rate does not differ from the average population crime rate.

(h) In previous problems, we assumed the x distribution was normal or approximately normal. Do we need to make such an assumption in this problem? Why or why not? Hint: Use the central limit theorem.

Yes. According to the central limit theorem, when n ≥ 30, the x distribution is approximately normal.

Yes. According to the central limit theorem, when n ≤ 30, the x distribution is approximately normal.     

No. According to the central limit theorem, when n ≥ 30, the x distribution is approximately normal.

No. According to the central limit theorem, when n ≤ 30, the x distribution is approximately normal.

2. The IQ of humans is approximately normally distributed with a mean 100 and standard deviation of 15. A. What is the probablitlty that a randomly selected person has an IQ greater than 105? B. What is the probablitlty that a SPS of 60 randomly selected people will have a mean IQ greater than 105?

3. A 95% confidence interval for a population mean is (57,65). Can you reject the null hypothesis the mean= 68 at the 5% significance level why or why not?