A manufacturer produces piston rings for an automobile engine. It is known that ring diameter is Normally Distributed with ? = 0.001 ??. A random sample of 9 rings has a mean diameter of ? = 74.036 ??

a. What is a 95% ?????????? ???????? for the true mean diameter of the piston rings. Use the given ? = 0.001 ??.

b. Interpret the ?????????? ???????? constructed in part (a)

c. For mathematical purposes, assume for a moment that the given standard deviation is the sample standard deviation, ? = 0.001. Construct a new 95% ?????????? ???????? using the sample standard deviation.

d. Compare your answers in (a) and (c), and explain why do you agree or disagree with the statement: “the ? ?????????? ????????? are wider than the ? ?????????? ?????????”.

e. The standard deviation calculated for the sample was found to be, ? = 0.0025. Use the calculated sample standard deviation and construct a new 95% ?????????? ????????.

Celebrities always seem to be getting divorced. The (approximate) lengths of some celebrity marriages in days are: 240 (J-Lo and Cris Judd), 144 (Charlie Sheen and Donna Peele), 143 (Pamela Anderson and Kid Rock), 72 (Kim Kardashian, if you can call her a celebrity), 30 (Drew Barrymore and Jeremy Thomas), 26 (W. Axl Rose and Erin Everly), 2 (Britney Spears and Jason Alexander), 150 (Drew Barrymore again, but this time with Tom Green), 14 (Eddie Murphy and Tracy Edmonds), 150 (Renée Zellweger and Kenny Chesney), 1657 (Jennifer Aniston and Brad Pitt). Compute the mean, median, standard deviation, range and interquartile range for these lengths of celebrity marriages.

A clinical trial was conducted using a new method designed to increase the probability of conceiving a girl. As of this​ writing, 963 babies were born to parents using the new​ method, and 887 of them were girls. Use a 0.05 significance level to test the claim that the new method is effective in increasing the likelihood that a baby will be a girl. Identify the null​ hypothesis, alternative​ hypothesis, test​ statistic, P-value, conclusion about the null​ hypothesis, and final conclusion that addresses the original claim. Use the​ P-value method and the normal distribution as an approximation to the binomial distribution.

What is the test statistics?

t=_ (round to two decimal places as needed.)

P-value is =_ (round to four decimal places as needed.)

1. Test the following hypotheses and also state the alternate hypothesis in each case. Write a sentence or two summarizing your conclusion after you have completed each hypothesis testing.

Hypothesis 1 The average time spent per table in Location A is the same as the average time spent per table in Location B.

Hypothesis 2 The average time spent per table in Location A is more than the average time spent per table in Location B.

Hypothesis 3 The average time spent per table in Location A is less than the average time spent per table in Location B.

Hypothesis 4 The average time spent per table in Location A is the same as the average time spent per table in Location C.

Hypothesis 5 The average time spent per table in Location A is the same as the average time spent per table in Location D.

Hypothesis 6 The average time spent per table in Location B is the same as the average time spent per table in Location C.

Hypothesis 7 The average time spent per table in Location B is the same as the average time spent per table in Location D.

Hypothesis 8 The average time spent per table in Location C is the same as the average time spent per table in Location D.

Hypothesis 9 The variance of time spent in Location A is the same as the variance of time spent in Location B.

Hypothesis 10 The variance of time spent in Location A is the same as the variance of time spent in Location C.

Hypothesis 11 The variance of time spent in Location A is the same as the variance of time spent in Location D.

Hypothesis 12 The variance of time spent in Location B is the same as the variance of time spent in Location C.

Hypothesis 13 The variance of time spent in Location B is the same as the variance of time spent in Location D.

Hypothesis 14 The variance of time spent in Location C is the same as the variance of time spent in Location D.

Hypothesis 15 The average time spent per table in ALL locations is exactly equal to each other. Hint: You will have to perform an ANOVA here.

4. Overall, what proporrtion of the tables are occupied for at least 75 mimutes? Construc a 95% confidence interval of the proportion of tables that are occupied for 75 minutes or more. HInt: Consult the materials on confidence interval for population proportion.
5. Write a short essay (no more than a page articulating the insight that you gained after doing the data analysis. What managerial action (if any) would you recommend based on your results?

Question Set 2: Two Independent Means Answer the following questions using the NYC2br.MTW file. You can find this dataset in this assignment in Canvas (i.e., where you downloaded this document and where you’ll upload your completed lab). Data were collected from a random sample of two-bedroom apartments posted on Apartments.com in Manhattan and Brooklyn.

A. What is one type of graph that could be used to compare the monthly rental rates of these two-bedroom apartments in Manhattan and Brooklyn? Explain why this is an appropriate graph. [10 points]

B. Using Minitab Express, Construct the graph you described in part A to compare the Manhattan and Brooklyn apartments in this sample. [10 points]

C. Use the five-step hypothesis testing procedure given below to determine if the mean monthly rental rates are different in the populations of all Manhattan and Brooklyn two-bedroom apartments. If assumptions are met, use a t distribution to approximate the sampling distribution. You should not need to do any hand calculations. Use Minitab Express and remember to include all relevant output. [30 points]

Step 1: Check assumptions and write hypotheses

Step 2: Calculate the test statistic

Step 3: Determine the p value

Step 4: Decide to reject or fail to reject the null hypothesis

Step 5: State a real-world conclusion

NYC2br.MTW file. - Data Set

Area Rent Address

1. The data in BUSI1013 Credit Card Balance.xlsx is collected for building a regression model to predict credit card balance of retail banking customers in a Canadian bank. Use this data to perform a simple regression analysis between Account balance and Income (in thousands). (12 points)
2. Develop a scatter diagram using Account Balance as the dependent variable y and Income as the independent variable x.
3. Develop the estimated regression equation.
4. Use the estimated regression equation to predict the Account Balance of a customer with Income of $58 thousands.
5. Use the critical-value approach to perform an F test for the significance of the linear relationship between account balance and Income at the 0.05 level of significance.
6. What percentage of the variability of Account Balance can be explained by its linear relationship with Income?
7. Use the p-value approach to perform a t test for the significance of the linear relationship between Account Balance and Income at the 0.05 level of significance.

Find the variance for the given sample data. Round your answer to one more decimal place than the original data. 3) The weights (in ounces) of 10 cookies are shown. 1.4 0.99 1.37 0.58 0.68 0.57 1.1 0.96 1.2 1.27

A simple random sample of size n is drawn from a population that is normally distributed. The sample mean is found to be 108, and the sample standard deviation is found to be 10. Construct the 96% confidence interval if the sample size is 25.

a. Construct the 96% confidence interval if the sample size is 10.

b. How does decreasing the sample size affect the margin of error?

c.Could you have computed the confidence intervals in a. and b.

d. if the population was not normal? Explain your answer.

True or False

A. In hypothesis testing, if you fail to reject the null hypothesis, then you have proven the null hypothesis to be true.

B. If you are more concerned about a type I error than a type II error in a hypothesis test, it would be better to use ∝= .01 than ∝= .10.

C. If you have complete information for a population (from a census), it would be unnecessary and inappropriate to carry out a hypothesis test about it.

D. The central limit theorem states that when n is large, the sampling distribution of xത is well approximated by a normal curve, even when the population distribution is not normal.

Same-sex marriage: In a recent ABC News/Washington Post poll, 1377 adults nationwide answered the question, “Overall, do you support or oppose allowing gays and lesbians to marry legally?”

Of the respondents, 476 support same-sex marriage. What is the 95% confidence interval for the proportion of all American adults who support same-sex marriage?

http://www.washingtonpost.com/page/2010-2019/WashingtonPost/2015/04/23/National-Politics/Polling/release_395.xml

1. (0.321, 0.371)
2. (0.333, 0.358)
3. (0.325, 0.367)
4. (0.313, 0.379)

The manager of a computer retails store is concerned that his suppliers have been giving him laptop computers with lower than average quality. His research shows that replacement times for the model laptop of concern are normally distributed with a mean of 4.5 years and a standard deviation of 0.6 years. He then randomly selects records on 29 laptops sold in the past and finds that the mean replacement time is 4.2 years.

Assuming that the laptop replacement times have a mean of 4.5 years and a standard deviation of 0.6 years, find the probability that 29 randomly selected laptops will have a mean replacement time of 4.2 years or less.
P(M < 4.2 years) =  
Enter your answer as a number accurate to 4 decimal places. NOTE: Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.945 g and a standard deviation of 0.314 g. The company that produces these cigarettes claims that it has now reduced the amount of nicotine. The supporting evidence consists of a sample of 43 cigarettes with a mean nicotine amount of 0.864 g.

Assuming that the given mean and standard deviation have NOT changed, find the probability of randomly seleting 43 cigarettes with a mean of 0.864 g or less.
P(M < 0.864 g) =  
Enter your answer as a number accurate to 4 decimal places. NOTE: Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

The SAT test scores have an average value of 1200 with a standard deviation of 100. A random sample of 35 scores is selected for the study.

A) What are the shape, mean(expected value) and standard deviation of the sampling distribution of the sample mean for samples of size 35?

B) What is the probability that the sample mean will be larger than 1235?

C) What is the probability that the sample mean will fall within 25 points of the population mean?

D) What is the probability that the sample mean will be less than 1180?

A practitioner wants to know if Condition A and Condition B are equivalent.

94 subjects were studied for their response to Condition A and B.

Using 5% critical probability, can the practitioner conclude if there is significant difference in the response to both Conditions.

A practice tutorial session was conducted before the exam. The examiner wants to know if the practice tutorial session helped in increasing the percentage of students who passed.

Using 5% critical probability, can the examiner conclude if the test is effective.

A healthcare researcher wants to know if taking flu shot in October prevents flu from Dec -March. If the researcher uses 5% probability for rejection, can it be concluded that flu shot is effective.