(a) Use the Excel tab titled SHINGLES to construct 95% confident intervals for the mean pallet weight for each shingle company. (b) In practical terms, interpret both of these confident intervals individually. (c) Compare the two confidence intervals to each other and

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Refer to the accompanying data set of mean drive-through service times at dinner in seconds at two fast food restaurants. Construct a 99% confidence interval estimate of the mean drive-through service time for Restaurant X at dinner; then do the same for Restaurant Y. Compare the results.

Restaurant X   Restaurant Y
84   104
122   122
118   153
142   119
270   175
181   133
125   115
150   126
166   124
215   128
336   132
305   132
176   229
110   215
152   291
146   122
94   98
236   136
243   239
189   141
158   139
203   201
169   144
125   146
67   133
197   147
182   153
112   137
146   169
178   138
190   236
199   230
228   248
191   239
352   229
302   164
206   85
202   105
181   54
189   170
108   75
153   148
180   140
151   98
175   121
159   147
169   130
125   185
137   153
306   127

Passing the ball between two players during a soccer game is a critical skill for the success of a team. A random sample of passes made by the English and German teams in the 2010 World Cup was drawn, and the number of successful passes in each sample was counted. Is there any difference in accuracy if we assume a level of significance of .01? See data below:

Reject the null, there is no difference in accuracy

Do not reject the null, there is no difference in accuracy

Reject the null, there is a difference in accuracy

Do not reject the null, there is a difference in accuracy

1. Given the following data:

Number of patients = 3,293

Number of patients who had a positive test result and had the disease = 2,184

Number of patients who had a negative test, and did not have the disease = 997

Number of patients who had a positive test result, but did not have the disease = 55

Number of patients who had a negative test result, but who had the disease = 57

1. Create a complete and fully labelled 2x2 table (10)
2. Calculate the positive predictive value (5)
3. Calculate the negative predictive value (5)
4. Calculate the likelihood ratio for a positive test result (5)
5. Calculate the likelihood ratio for a negative test result (5)

In a 17 month period the powerball was drawn from a collection of 35 balls numbered 1-35. Total of 150 drawings were made. For the purpose of this exercise we grouped numbers into five categories. test the hypothesis that each of the categories is equally likely. Use the 0.025 level of signifigance and the critical value method with the table.

Category:|1-7| |8-14| |15-21| |22-28| |29-35|

Observed: |21 | 35 | | 33 | | 27 | | 34 |

Expected frequencies for each category????

1)What are expected frequencies?

2)Compute the value of x^2. Round the answer to three decimal places

3)How many degrees of freedom are there?

4)State the null and alternate hypotheses

H0= p1=p2=p3=p4=p5= _____

Some or all of the actual probabilities (differ or ____) from the specifies by H0

5)Find the critical value. Round the answer to three decimal places.

6)determine whether to reject H0

7)State a conclusion

There (is or is not) enough evidence to conclude that the distribution differs from what was expected.

Explain the influence of a level of significance and sample size has on hypothesis testing. Provide an example of the influence and how it impacts business decisions.

The accompanying data represent the total travel tax​ (in dollars) for a​ 3-day business trip in 8 randomly selected cities. A normal probability plot suggests the data could come from a population that is normally distributed. A boxplot indicates there are no outliers. Complete parts​ (a) through​ (c) below. 67.88 78.86 69.13 83.59 79.73 86.64 101.37 99.93 LOADING... Click the icon to view the table of critical​ t-values. ​(a) Determine a point estimate for the population mean travel tax. A point estimate for the population mean travel tax is ​$ nothing. ​(Round to two decimal places as​ needed.) ​(b) Construct and interpret a 95​% confidence interval for the mean tax paid for a​ three-day business trip. Select the correct choice below and fill in the answer boxes to complete your choice. ​(Round to two decimal places as​ needed.) A. One can be nothing​% confident that the mean travel tax for all cities is between ​$ nothing and  ​$ nothing. B. One can be nothing​% confident that the all cities have a travel tax between ​$ nothing and ​$ nothing. C. There is a nothing​% probability that the mean travel tax for all cities is between ​$ nothing and ​$ nothing. D. The travel tax is between ​$ nothing and ​$ nothing for nothing​% of all cities. ​(c) What would you recommend to a researcher who wants to increase the precision of the​ interval, but does not have access to additional​ data? A. The researcher could decrease the level of confidence. B. The researcher could increase the level of confidence. C. The researcher could decrease the sample standard deviation. D. The researcher could increase the sample mean. Click to select your answer(s).

A car dealership has 6 red, 11 silver and 5 black cars on the lot. Ten cars are randomly chosen to be displayed in front of the dealership. Complete parts (a) through (c) below. Please write clearly. Thank you!

A: find the probability that 4 cars are red and the rest are silver. (round to four decimal places as needed)

B: Find the probability that 5 cars are red and 5 are black. (round to six decimal places as needed)

C: Find the probability that exactly 6 cars are red. (round to five decimal places as needed)

Decide whether you can use the normal distribution to approximate the binomial distribution. If you​ can, use the normal distribution to approximate the indicated probabilities and sketch their graphs. If you​ cannot, explain why and use the binomial distribution to find the indicated probabilities. Five percent of workers in a city use public transportation to get to work. You randomly select 269 workers and ask them if they use public transportation to get to work.

(Complete parts A through D)

Can the normal distribution be used to approximate the binomial​ distribution?

a.​Yes, because both np ≥ 5 and nq ≥ 5.

b.​No, because np < 5.

c.​No, because nq <5.

A) ​- Find the probability that exactly 20 workers will say yes.

What is the indicated​ probability? (____) Round to four decimal places as​ needed.

Sketch the graph of the normal distribution with the indicated probability shaded.

B) ​- Find the probability that at least 7 workers will say yes.

What is the indicated​ probability? (____) Round to four decimal places as​ needed.

Sketch the graph of the normal distribution with the indicated probability shaded.

C) - Find the probability that fewer than 20 workers will say yes.

What is the indicated​ probability? (____) Round to four decimal places as​ needed.

Sketch the graph of the normal distribution with the indicated probability shaded.

D) - A transit authority offers discount rates to companies that have at least 30 employees who use public transportation to get to work. There are 452 employees in a company. What is the probability that the company will not get the​ discount?

Can the normal distribution be used to approximate the binomial​ distribution?

a.​ No, because nq < 5.

b.​ No, because np < 5.

c.​ Yes, because both np ≥ 5 and nq ≥ 5.

What is the probability that the company will not get the​ discount? (____) Round to four decimal places as​ needed.

Sketch the graph of the normal distribution with the indicated probability shaded.

On your first day on the job, your boss asks you to conduct a hypothesis test about the mean dwell time of a new type of UAV. Before you arrived, an experiment was conducted on n = 5 UAVs (all of the new type) resulting in a sample mean dwell time of (y bar)= 10.4 ℎours. The goal is to conclusively demonstrate, if possible, that the data supports the manufacturer’s claim that the mean dwell time is greater than 10 hours. Given that it is reasonable to assume the dwell times are normally distributed, the sample standard deviation is s = 0.5 ℎours, and using a significance level of alpha = 0.01, conduct the appropriate hypothesis test

Part A. Parameter of interest: From the problem context, identify the parameter of interest.

Part B Null hypothesis, H0: State the null hypothesis, H0 in terms of the parameter of interest H0:

Part C Alternative hypothesis, H1: Specify an appropriate alternative hypothesis, H1. H1:

Part D Test Statistic: Determine an appropriate test statistic (equation; state degrees if freedom if necessary).

Part E Reject H0 if: State the rejection criteria for the null hypothesis for the given level of α. OS3180 Probability and Statistics Final Exam Quarter 3 AY19 9

Part F Computations: Compute any necessary sample quantities, substitute these into the equations for the test statistic, and compute that value. Perform P-Value calculations.

Part G Draw conclusions: Decide whether or not H0 should be rejected and report that in the problem context. Make a “real-world” statement about the outcome of the test (cannot just say “reject the null hypothesis”)

Part H Provide an illustration of the hypothesis test you conducted above, making sure that you annotate: the confidence level, the significance level, the test statistic, the critical value, and the p-value.

Suppose you want to know the variance of the weights of the only five iguanas in a particular zoo. You measure their weights to be 8.3, 8.4, 8.6, 9.2, and 9.5 pounds (15 points) What was different between the population variance and the sample variance? Which is bigger? Why is there a need to have a different formula? Write at least five good sentences in answering this question. (3 points) The population standard deviation is the square root of the population variance. Calculate the population standard deviation using part (c): (3 points) The sample standard deviation is the square root of the sample variance. Calculate the sample standard deviation using part (d): __________ (15 points) What is the difference between the population standard deviation and the sample standard deviation? When do you use each one? Write at least five good sentences in answering this question. (17 points) What did you do differently between calculating the variance and the standard deviation? What does each measure? Write at least five good sentences in answering this question.

Dipper has a 10 year increasing annuity immediate that pays $100 at the end of the first year, $200 at the end of the second year, ... , and $1000 at the end of the 10th year. He exchanges the annuity for a perpetuity of equal value that pays X at the end of each year. If the effective annual interest rate is 3%, find the value of X

How to detect heteroscedasticity in the regression model? Look at the residual plots against each independent predictor. A “V” or “U” shape pattern indicates that the error terms do not have homogeneous variance. true or false

using R :-

A Gumbel random variable X has distribution function

FX (x) = exp (−e^−x).

a) Give a graph of FX and explain using this plot why FX is a valid cumulative probability distri-

bution function.

(b) Find the values of the first and third quartiles and median X and show their values on the graph.

(c) Make a table of x and FX (x) for x equal to the integers from −2 to 5.

(d) Find the probabilities P{−1 < X ≤ 4} and P{4 < X}.

(e) Find the probability density for this distribution function.

(f) Provide a second sketch of the distribution function along with a sketch of the density function indicating P {−1 < X ≤4} on both pl

Test the Business Major's hypothesis at the 5% significance level. The mean ‘Cost’ for a college is $160,000. Be sure to interpret your results.

• List your givens - n, standard deviation, alpha...
• Provide the formula you will use. Why are you using that formula? How does it fit the situation?
• Show how you have plugged in the numbers.
• What is your computed test statistic?
• Show the computation of the p value.
• Will you reject or fail to reject the null hypothesis. Why?