Suppose that weekly expenses for two student organizations are thought to be similar. A random sample of 10 weeks yields the following weekly expenses for each organization:

Organization A           Organization B

     $ 119.25                      $ 111.99

     $ 123.71                      $ 116.62

     $ 121.32                      $ 114.88

     $ 121.72                      $ 115.38

     $ 122.34                      $ 115.11

     $ 122.42                      $ 114.40

     $ 120.14                      $ 117.02

     $ 123.63                      $ 113.91

     $ 122.19                      $ 116.89

     $ 122.44                      $ 121.87

Use a Wilcoxon Rank Sum Test to determine whether expenses differ for the two organizations. Test at the 0.05 level.

A bank president claims that the median of debt-to-equity ratio of commercial loans provided is less than 5. A random sample of 15 commercial loans is selected with the following values for this ratio:

1.31                 1.33                 1.22

1.78                 1.45                 1.32

1.46                 1.41                 1.19

1.05                 1.29                 1.11

1.37                 1.21                 1.65

Use a Sign Test at the 0.05 level to test this claim. Do this by hand and not using Excel.

In analyzing hits by bombs in a past war, a city was subdivided into 471 regions, each with an area of 0.5-km². A total of 390 bombs hit the combined area of 471 regions. The Poisson distribution applies because we are dealing with the occurrences of an event (bomb hits) over some interval (a region with area of 0.5-km².

A small branch bank has two tellers, one for deposits and one for withdrawals. Customers arrive at each teller’s window with an average rate of 18 customers per hour. (The total customer arrival rate is 36 per hour.) The interarrival times are exponential. The service time of each teller is exponential with a mean of 3 minutes. The bank manager is considering changing the setup to allow each teller to handle both withdrawals and deposits to avoid the situations that arise from time to time when the queue is sizable in front of one teller while the other is idle. However, since the tellers would have to handle both deposits and withdrawals, their efficiency would decrease to a mean service time of 3.2 minutes. Compare the present system with the proposed system with respect to the total average number of customers in the banks and the average time a customer would have to spend in the bank.

1. A random sample of 40 college student students shows that the score of a College Statistics is normally distributed with its mean, 81 and standard deviation, 8.4. Find 99 % confidence interval estimate for the true mean.

The data in the worksheet provides the number of defects produced in a series of panels. a. Construct a C-chart for this process. b. Does the process appear to be in control? Why or why not?

As a binomial question: Flip a coin twice. The probability of observing a head is 50%, what is the probability that I observe 1 head? binompdf (n, p, x) so binompdf( 2, .50,1) Sampling Proportion question (8.2): There is a 50% of observing a head. If we flip the coin 100 times, what is that at most 30% of the flips will be heads? n*p*(1-p) =100*.50*.50=25 (Do not use my coin example. Use your own scenario). pˆ=.30 po or μ=50 Image result for sample proportion z formula NormalCDF (-999,.30,.50,.05) raw numbers z=.30−.50.50(1−.50)100√=−.20.05=−4 NormalCDF(-999,-4) standardized that means the mean is 0 and standard deviation is 1.

I need a similar example of this question?

The Student's t distribution table gives critical values for the Student's t distribution. Use an appropriate d.f. as the row header. For a right-tailed test, the column header is the value of α found in the one-tail area row. For a left-tailed test, the column header is the value of α found in the one-tail area row, but you must change the sign of the critical value t to −t. For a two-tailed test, the column header is the value of α from the two-tail area row. The critical values are the ±t values shown.

Pyramid Lake is on the Paiute Indian Reservation in Nevada. The lake is famous for cutthroat trout. Suppose a friend tells you that the average length of trout caught in Pyramid Lake is μ = 19 inches. However, a survey reported that of a random sample of 51 fish caught, the mean length was x = 18.5 inches, with estimated standard deviation s = 2.8 inches. Do these data indicate that the average length of a trout caught in Pyramid Lake is less than μ = 19 inches? Use α = 0.05. Solve the problem using the critical region method of testing (i.e., traditional method). (Round the your answers to three decimal places.)

An article contained the following observations on degree of polymerization for paper specimens for which viscosity times concentration fell in a certain middle range:

(a) Construct a boxplot of the data.

Comment on any interesting features. (Select all that apply.)

The data appears to be centered near 428.There are no outliers.The data appears to be centered near 438.There is one outlier.There is little or no skew.The data is strongly skewed.

(b) Is it plausible that the given sample observations were selected from a normal distribution?

YesNo    

(c) Calculate a two-sided 95% confidence interval for true average degree of polymerization. (Round your answers to two decimal places.)

  ,

Does the interval suggest that 443 is a plausible value for true average degree of polymerization?

YesNo    

Does the interval suggest that 450 is a plausible value?

YesNo    

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 409.0 gram setting. Based on a 36 bag sample where the mean is 414.0 grams, is there sufficient evidence at the 0.05 level that the bags are overfilled? Assume the standard deviation is known to be 26.0.

Step 1: Enter the hypotheses:

Ho:___________________

Ha:___________________

Step 2: Find the value of the test statistic. Round your value to three decimal places

Step 3: Specify if the test is one tailed or two tailed

Step 4: Determine the decision rule for rejecting the null hypothesis. Round your value to three decimal places.

Step 5. Enter the value of the level of significance.

Step 6: Make the decision to reject or fail to reject the Null hypothesis.

(A) Reject the null hypothesis

(B) Fail to reject the null hypothesis

A study of arrival times for a number of international flights. The times were randomly recorded from a normally distributed population with the following results:

n = 19 and s = 12.1. Find the 95% confidence interval for σ.

To ensure Fork-lifts are not over-loaded, design engineers have to consider the weights of cargo. Suppose 400 cargo shipments have normally distributed weights with a mean of 500 pounds and a standard deviation of 25 pounds. Given a confidence level of 95%:

a) What is the error of estimate (E)?

b) What does the sample size have to be if we want the error of estimate to be no more than 1.5?

You are interested in knowing the proportion of people that are observing the CDC guidelines for social distancing during the COVID-19 pandemic. You survey 100 randomly selected people and find that 80 have followed the guidelines.

Construct a 95% confidence interval around the unknown true proportion of people following the guidelines. CALCULATE THE UPPER LIMIT in this question. Use 4 digits of precision

Use the R code below to help you.

> qnorm(0.90)
[1] 1.282
> qnorm(0.95)
[1] 1.645
> qnorm(0.975)
[1] 1.960
> qnorm(0.99)
[1] 2.326
> pnorm(0.90)
[1] 0.8159
> pnorm(0.95)
[1] 0.8289
> pnorm(0.975)
[1] 0.8352
> pnorm(0.99)
[1] 0.8389

One representative from the CDC claimed that as many as 25% of people who have Covid-19 may not be showing any symptoms. If this is true, what is the probability of randomly choosing 450 people who are experiencing no symptoms and 110 or less of them actually have the virus?

Make sketches and label all variables and give the appropriate calculator command.

What is the inequality that must be true in order to treat the sample proportions in this problem as being normally distributed?

The average time to run the 5K fun run is 21 minutes and the standard deviation is 2.5 minutes. 13 runners are randomly selected to run the 5K fun run. Round all answers to 4 decimal places where possible and assume a normal distribution.

1. What is the distribution of XX? XX ~ N(,)
2. What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
3. What is the distribution of ∑x∑x? ∑x∑x ~ N(,)
4. If one randomly selected runner is timed, find the probability that this runner's time will be between 20.2599 and 21.0599 minutes.
5. For the 13 runners, find the probability that their average time is between 20.2599 and 21.0599 minutes.
6. Find the probability that the randomly selected 13 person team will have a total time less than 266.5.