A 90 % confidence interval (a t interval) for the mean lives (in minutes) of Kodak AA batteries is ( 480, 520 ). Assume that this result is based on a sample of size 25

a. value of sample standard deviation

b. 99% confidence interval

c. If the confidence interval (482.6156 ,517.3844) is obtained from the same sample data, what is the degree of confidence?

A car company advertises that thir Super Spiffy Sedan averages 29mpg (miles per gallon). You randomly select a sample of Super Spiffies from local car dealerships and test their gas mileage under similar conditions.

You get the following MPG scores:

33 27 32 34 34 28 27 31

Note: SSx = 63.50

Using alpha =.01, conduct the 8 steps to hypothesis testing to determine whether the actual gas mileage for these cars differs significantly from 29mpg.

Suppose a carnival director in a certain city imposes a height limit on an amusement park ride called Terror Mountain, due to safety concerns. Patrons must be at least 4 feet tall to ride Terror Mountain. Suppose patrons’ heights in this city follow a Normal distribution with a mean of 4.5 feet and a standard deviation of 0.8 feet (patrons are mostly children). Make sure to show all of your work in this question. Show the distribution that your random variable follows; state the probability you are asked to calculate; show any tricks you use; show how you standardize, and state your found value from Table A4.

a) [5 marks] What is the probability that a randomly selected patron would be tall enough to ride Terror Mountain?

b) [5 marks] A group of 3 friends want to ride Terror Mountain. What is the probability that their mean height is greater than 4.5 feet?

c) [7 marks] Another group of 5 friends wants to ride Terror Mountain. What is the probability that their mean height is between 4 and 4.25 feet, inclusive?

Suppose you want to determine the average height of college basketball players in NCAA Division I. In a random sample of 9 players, the sample average is 70.725 inches with a standard deviation of 4.4081 inches. What is the 95% confidence interval for the average height of all NCAA D-I players?

Question 6 options:

A new drug to treat high cholesterol is being tested by pharmaceutical company. The cholesterol levels for 8 patients were recorded before administering the drug and after. The mean difference in total cholesterol levels (after - before) was 24.523 mg/dL with a standard deviation of 19.3919 mg/dL. Create a 90% confidence interval for the true average difference in cholesterol levels by the drug.

Question 9 options:

A suggestion is made that the proportion of people who have food allergies and/or sensitivities is 0.57. You believe that the proportion is actually greater than 0.57. The hypotheses for this test are Null Hypothesis: p ≤ 0.57, Alternative Hypothesis: p > 0.57. If you select a random sample of 21 people and 10 have a food allergy and/or sensitivity, what is your test statistic and p-value?

Question 11 options:

Please answer all of the questions

A consumer wanted to find out how accurate Siri (an Apple digital assistant) is, so he asked questions on general facts and recorded how many Siri got right. Out of the 299 questions, he asked Siri, Siri responded correctly to 132 of them. What is the estimate of the population proportion? What is the standard error of this estimate?

Question 1 options:

Question 2 (1 point)

Historically, 72.98% of packages delivered by UPS are on time. Suppose 151 deliveries are randomly selected for quality control. What is the probability that less than 74.48% of the deliveries were on time?

Question 2 options:

Question 3 (1 point)

Fill in the blank. In a drive thru performance study, the average service time for McDonald's is 186.69 seconds with a standard deviation of 6.26 seconds. A random sample of 82 times is taken. There is a 43% chance that the average drive-thru service time is greater than ________ seconds.

Question 3 options:

Question 4 (1 point)

Experimenters injected a growth hormone gene into thousands of carp eggs. Of the 234 carp that grew from these eggs, 34 incorporated the gene into their DNA (Science News, May 20, 1989). With a confidence of 90%, what is the margin of error for the proportion of all carp that would incorporate the gene into their DNA?

Question 4 options:

The fatality rate is estimated at 2% across all age groups. Suppose a random sample of 200 infected persons is selected. (round probabilities to 4 decimal places)

What is the probability that between 4 and 8 infected people die?

Would it be considered unusual if less 2 infected people die? Justify your answer.

Regression analysis is often used in accounting to estimate costs. By collecting data on volume and cost and using the least squares method to develop an estimated regression equation relating volume and cost, an accountant can estimate the cost associated with a particular manufacturing volume. The following sample of production volumes and total cost data for a manufacturing operation was collected:

Use Excel and the MegaStat add-in to answer the following questions.

What percent of the variation in total cost can be explained by production volume? Report your answer to 4 decimal places, using conventional rounding rules.

ANSWER:      %

The company’s production schedule shows 575 units must be produced next month. What is the predicted total cost for this operation? Report your answer to 2 decimal places, using conventional rounding rules.

ANSWER:      $

What is the 98% prediction interval for the total cost for next month, when 575 units must be produced? Report your answer to 2 decimal places, using conventional rounding rules.

ANSWER:      Lower confidence limit =              Upper confidence limit =

What is the 98% confidence interval for the mean total cost for all months where 575 units must be produced? Report your answer to 2 decimal places, using conventional rounding rules.

ANSWER:      Lower confidence limit =              Upper confidence limit =

The AMS technical services department has embarked on a quality improvement effort. Its first project relates to maintaining the target upload speed for its Internet service subscribers. Upload speeds are measured on a standard scale which the target value is 1.0. Data collected over the past year indicate that the upload speed is approximately normally distributed, with a mean of 1.005 and a standard deviation of 0.10. Each day, one upload speed is measured. The upload speed is considered acceptable if the measurement on the standard scale between 0.95 and 1.05.

1. Assuming that the distribution has not changed from what it was in the past year, what is the probability that the upload speed is

a. less than 1.0?
b. between 0.95 and 1.0?
c. between 1.0 and 1.05?
d. less than 0.95 or greater than 1.05?

2.) The objective of the operations team is to reduce the probability that the upload speed is below 1.0. Should the team focus on process improvement that increases the mean upload speed 1.05 or on process improvement that reduces the standard deviation of the upload speed to 0.075? Explain

Sometimes both x-bar chart and p-chart are available to monitor the same process. In Table 1 above, you collect measurement data (wait times in minutes) to create an x-bar chart. You can also collect count data (pass/fail data) instead to create a p-chart. As you are curious about how it works, you decide to create a p-chart, too.

First, you convert the measurement data in Table 1 to count data using the following criteria:

For example, the third wait time on Day 1 in Table 1 is 21 minutes. This is less than 25 minutes. Therefore, you count this as a defective. Table 2 shows the number of defectives.

Table 2: Number of Defectives

Question 1

Based on the Table 2, determine the probability of defectives (p).

1. p=0.35
2. p=1.40
3. p=3.50
4. p=5.60
5. p=14.00

Question 2

Continued from Question 1. Determine the standard deviation of p (σ_p). Round your answer to two decimal places.

1. σ_p = 0.02
2. σ_p = 0.08
3. σ_p = 0.15
4. σ_p = 0.24
5. σ_p = 0.37

Question 3

Continued from Question 14. Determine three-sigma (i.e., z=3) upper and lower control limits for a p-chart. Round your answers to two decimal places.

1. LCL=0.28, UCL=2.52
2. LCL=0, UCL=1.07
3. LCL=0, UCL=0.80
4. LCL=0.12, UCL=0.58
5. LCL=0.28, UCL=0.42

Question 4

Based on the p-chart, is the process in control? If not, which day(s) is not in control?

1. Yes. The process is in control.
2. No. Day 4 is not in control.
3. No. Day 3 and Day 4 are not in control.
4. No. Day 2, Day 3 and Day 4 are not in control.
5. No. All days are not in control.

* I assume that customer wait times (population) are normally distributed with a mean of 30 minutes and a standard deviation of 5 minutes. This implies that the mean of customer wait times (sample mean) is normally distributed with a mean of 30 minutes and a standard deviation of 510 minutes, where 10 is the number of observations in each sample (i.e., sample size). Then, the upper and lower thresholds are calculated as 30±3510. *

select a recurring quantity from your OWN life for which you have monthly
records at least 2 years (including 24 observation in dataset at least). This might be the cost of a
utility bill, the number of cell phone minutes used, or even your income.
If you do not have access to such records, use the internet to find similar data, such as average
monthly housing prices, rent prices in your area for at least 2 years (You must note the data
source with an accessible link). Data can also be monthly sales of some particular commodity.
1.4 Please do the descriptive analysis, using the method of index number and Exponential
Smoothing individually. And try to explain the pattern you find.
1.5 Use two methods you learned to predict the value of your quantity for the next year (12
months). And make comparison with two results.

It appears that over the past 50 years, the number of farms in the United States declined while the average size of farms increased. The following data provided by the U.S. Department of Agriculture show five-year interval data for U.S. farms. Use these data to develop the equation of a regression line to predict the average size of a farm by the number of farms Discuss the slope and y-intercept of the model.

Based on experience on average 10 customers enter the store every 30 mins. To verify this assumption, she has recorded the customer's foot traffic for 5 hours.

- run a hypothesis testing to check if the average number of customers per 30 min is greater than 10 customers per 30 min

H₀ = No of customers or 30 min is NOT greater than 10

H₁ = No of customers or 30 min is greater than 10

Q: What is the test statistics of this hypothesis testing? (Based on a significance level of 10%, can we reject the null hypothesis?) And what is the correlation value between number of customers entering the store and number of purchased items?

Researchers studying the human voice measure the volume in decibels. Normal conversation occurs at around

50 decibels but some singers can reach over 100 decibels. The researchers choose a random sample of 25

professional opera singers and record the maximum volume reached by each. They find the mean volume for

this sample is 98 decibels with a standard deviation of 10 decibels. Carry out a hypothesis test with alpha= 0.05,

to determine if the mean maximum volume of all professional opera singers is 100 decibels.

WinCo Foods, a large discount grocery retailer in the Western United States, promotes itself as the lowest priced grocery retailer. In newspaper ads WinCo Foods published a price comparison for products between WinCo and several competing grocery retailers. One of the retailers compared against WinCo was Walmart, also known as a low price competitor. WinCo selected a variety of products, listed the price of the product charges at each retailer, and showed the sales receipt to prove the prices at WinCo were the lowest in the area. A sample of the products and their price comparison at both WinCo and Walmart are shown on the left. Do the prices listed indicate that, on average, prices at WinCo are lower than prices at Walmart? Use 5% significance level.

Solve this question using Excel. State the null & alternative hypotheses clearly. Interpret the Excel output and state your conclusion clearly. Provide all your results and comments on this sheet. Specifically, type in your answers in the spaces provided below:

Are the samples related (i.e. dependent) or independent?

Null Hypothesis:

Alternative Hypothesis:

Interpretation of Excel output (Conclusion of Hypothesis test):

Business Implications:

The researcher from the Annenberg School of Communications is interested in studying the factors that influence how much time people spend talking on their smartphones. She believes that gender might be one factor that influences phone conversation time. She specifically hypothesizes that women and men spend different amounts of time talking on their phones. The researcher conducts a new study and obtains data from a random sample of adults from two groups identified as women and men. She finds that the average daily phone talking time among 15 women in her sample is 42 minutes (with a standard deviation of 6). The average daily minutes spent talking on the phone among 17 men in her sample is 38 (with a standard deviation of 5). She selects a 95% confidence level as appropriate to test the null hypothesis.

What decision should the researcher make about the null hypothesis? Be sure to explain your answer

Please interpret the research findings, making sure to reference:

- whether the relationship is statistically significant

- whether we can say there is an association between the independent and dependent variable in the population

Would our decision about the null hypothesis have been different if the researcher had initially hypothesized that women spend more time talking on their phones than men?

Explain all parts/information necessary to answer this question.