A researcher has boiled her hypothesis test down to the following information.

H0: p=0.7, Ha: p<0.7, α=0.02 x=117, n=172

Find the p-value.

3.

a. A researcher wants to study how long (in days) patients aged 30-39 who are admitted to a hospital for coronavirus treatment spend in the hospital before being discharged. Preliminary data suggests that
? = 4 days is a safe assumption. Assuming the recovery times have standard deviation 4 days (which would say that virtually all patients recover in some number of days +/- about 12 days), use the formula

? = ?^2 * ?^2 / ?^2

To find the number of patients that would need to be sampled to construct a 95% confidence interval for the mean recovery time with a margin of error of 0.5 days. Make sure to show how you find the critical value z

b. Same question as part a, if instead you assume that ? = 3.5 days.

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim.

A safety administration conducted crash tests of child booster seats for cars. Listed below are results from those​ tests, with the measurements given in hic​ (standard head injury condition​ units). The safety requirement is that the hic measurement should be less than 1000 hic. Use a 0.010.01 significance level to test the claim that the sample is from a population with a mean less than 1000 hic. Do the results suggest that all of the child booster seats meet the specified​ requirement?

645645     602602     12201220     591591     579579     539539

b) Identify the test statistic.

c)Identify the​ P-value.

Text exercise 39 page 638. This question uses the same data as exercise 2 above, and the data is in the accompanying spreadsheet.

(a) Estimate the regression in Excel and report the regression line.                                  [2 pts]

(b) Calculate a  95% confidence interval for the forecast of the average amount spent on entertainment at a city where the room rate is $89.                                                       [3 pts]

(b) Calculate a  90% confidence interval for the forecast of the idiosyncratic amount spent on entertainment at a city where the room rate is the average rate of $128.                        [3 pts]

(d) Use a t-test to test the hypothesis that there is a 1 to 1 relationship between entertainment expenses and hotel expenses. (ie test H0: β=1)                                                    

DATA:

Use the following information to answer the next five exercises: A poll of 1,200 voters asked what the most significant issue was in the upcoming election. Sixty-five percent answered the economy. We are interested in the population proportion of voters who feel the economy is the most important. Using Excel and functions. Don't forget to use this formula sqrt(p'*(1-p')/n) =

1. Define the random variable X in words.

2. Define the random variable P′ in words.

3. Which distribution should you use for this problem?

4. Construct a 90% confidence interval, and state the confidence interval and the error bound.

5. What would happen to the confidence interval if the level of confidence were 95%?

1. Use z-scores to standardize the values, and then calculate the Euclidean distance between the first two observations.

2.  Use the min-max transformation to normalize the values, and then calculate the Euclidean distance between the first two observations.

Provide all relevant Minitab output, and make sure the responses are organized and are clearly written.

Suppose an investigator is interested in the weight (pounds) of a certain type of fish. They collect a random sample of 26 fish from a lake. The resulting data is compiled in the table below. Assume the data is normally distributed.

Observation | Weight 1 11.73 2 13.33 3 12.65 4 12.54 5 12.67 6 10.55 7 13.24 8 11.09 9 12.28

10 12.38 11 10.26 12 10.03 13 11.18

Table 1: Weight data
Obs Weight

14 10.97 15 12.16 16 10.93 17 12.27 18 11.86 19 10.47 20 11.96 21 10.67 22 11.01 23 11.47 24 9.24 25 11.58 26 12.42

1) Using Minitab produce descriptive statistics for the weight of the fish in the sample. Include the median, Quartile 1, Quartile 3, maximum value, minimum value, mean, standard deviation, and variance.

2) Using Minitab, produce a 95% confidence interval for the population mean weight.

3)Consider the investigator is interested in performing a hypothesis test to determine if the population average weight is less than 12 pounds at the α = .05 significance level.
a) Using the formula from class and the descriptive statistics above, calculate the value of the test statistic for this experiment.

b) What is the numeric value of the critical value for this hypothesis test? (Step 3 of hypothesis tests)
c) Implement this hypothesis test in Minitab. In the results, highlight or circle the test statistic and p-value.
d) Using both the p-value and critical value approach from above, state your conclusion for this experi- ment, and explain your reasoning for choosing that conclusion.

Let x be the age in years of a licensed automobile driver. Let y be the percentage of all fatal accidents (for a given age) due to speeding. For example, the first data pair indicates that 39% of all fatal accidents of 17-year-olds are due to speeding.

Complete parts (a) through (d), given

Σx = 329, Σy = 117, Σx² = 18,263, Σy² = 2825, Σxy = 4029, and r ≈ −0.942.

(a) Find x, and y. Then find the equation of the least-squares line  = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.)

(b) Find the value of the coefficient of determination r². What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (Round your answer for r² to three decimal places. Round your answers for the percentages to one decimal place.)

c) Predict the percentage of all fatal accidents due to speeding for 35-year-olds. (Round your answer to two decimal places.)
%

(d)Use a calculator to verify that

x = 63,

x² = 1079,

y = 640,

y² = 91,738,

and

xy = 9,677.

Compute r. (Round your answer to three decimal places.)

PLEASE WRITE THE ANSWER CLEAR

You are competing for a contract in a second-price auction. The cost for you to fulfill the contract is $10m. Check if each of the following statements is true. If not, change the statement to make it correct.

1. If with probability 0.4, the lowest cost of your competitors is $6m and with probability 0.6, it is $15m. Then your expected profit from the auction is $1.4m.

2. (4 points) If one of your competitors can fulfill the contract at cost $7m, then you are going to lose at least $3m.

3. (4 points) If 30% of chance that one of your competitors has a cost below $6m, 30% of chance that all of them have a cost above $16m, and 40% of chance all of them have a cost somewhere between $8m and $11m. Then your expected profit is at least $1.8m.

4. (4 points) If all your competitors inflate their ask prices above their costs by 10%, then you will be worse if you do not do so.

1/Suppose that about 84% of graduating students attend their graduation. A group of 37 students is randomly chosen, and let X be the number of students who attended their graduation.

Please show the following answers to 4 decimal places.

1. What is the distribution of X? X ~ ? B U N  (,)
2. What is the probability that exactly 29 number of students who attended their graduation in this study?
3. What is the probability that at least 29 number of students who attended their graduation in this study?
4. What is the probability that more than 29 number of students who attended their graduation in this study?
5. What is the probability that between 26 and 31 (including 26 and 31) number of students who attended their graduation in this study?

2/A company prices its tornado insurance using the following assumptions:
• In any calendar year, there can be at most one tornado.
• In any calendar year, the probability of a tornado is 0.13.
• The number of tornadoes in any calendar year is independent of the number of tornados in any other calendar year.
Using the company's assumptions, calculate the probability that there are fewer than 4 tornadoes in a 23-year period

3/A local bakary has determined a probability distribution for the number of cheesecakes that they sell in a given day.

What is the probability of selling 15 cheesecakes in a given day?
What is the probability of selling at least 10 cheesecakes?
What is the probability of selling 5 or 15 chassescakes?
What is the peobaility of selling 25 cheesecakes?
Give the expected number of cheesecakes sold in a day using the discrete probability distribution?
What is the probability of selling at most 10 cheesecakes?

4/Find the mean of the following probability distribution? Round your answer to four decimal places.

μμ =

5/

A researcher gathered data on hours of video games played by school-aged children and young adults. She collected the following data.

Find the range.
( ) hours
Find the standard deviation. Round your answer to the nearest tenth, if necessary.
( ) hours
Find the five-number summary.

.

Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Then x has a distribution that is approximately normal with mean μ = 64.0 kg and standard deviation σ = 7.7 kg. Suppose a doe that weighs less than 55 kg is considered undernourished.

(a) What is the probability that a single doe captured (weighed and released) at random in December is undernourished? (Round your answer to four decimal places.) Incorrect: Your answer is incorrect.

(b) If the park has about 2250 does, what number do you expect to be undernourished in December? (Round your answer to the nearest whole number.) Incorrect: Your answer is incorrect. does

(c) To estimate the health of the December doe population, park rangers use the rule that the average weight of n = 55 does should be more than 61 kg. If the average weight is less than 61 kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weight x for a random sample of 55 does is less than 61 kg (assuming a healthy population)? (Round your answer to four decimal places.) Incorrect: Your answer is incorrect.

(d) Compute the probability that x < 65.1 kg for 55 does (assume a healthy population). (Round your answer to four decimal places.)

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

The increasing annual cost (including tuition, room, board, books, and fees) to attend college has been widely discussed (Time.com). The following random samples show the annual cost of attending private and public colleges. Data are in thousands of dollars.

(a)

Compute the sample mean (in thousand dollars) and sample standard deviation (in thousand dollars) for private colleges. (Round the standard deviation to two decimal places.)

sample mean$  thousandsample standard deviation$  thousand

Compute the sample mean (in thousand dollars) and sample standard deviation (in thousand dollars) for public colleges. (Round the standard deviation to two decimal places.)

sample mean$  thousandsample standard deviation$  thousand

(b)

What is the point estimate (in thousand dollars) of the difference between the two population means? (Use Private − Public.)

$  thousand

Interpret this value in terms of the annual cost (in dollars) of attending private and public colleges.

We estimate that the mean annual cost to attend private colleges is $  more than the mean annual cost to attend public college

(c)

Develop a 95% confidence interval (in thousand dollars) of the difference between the mean annual cost of attending private and public colleges. (Use Private − Public. Round your answers to one decimal place.)

$  thousand to $  thousand

Research in the gaming industry showed that 8% of all slot machines in the United States stop working each year. Short’s Game Arcade has 70 slot machines and only 5 failed last year. Use the five-step hypothesis-testing procedure at the 0.05 significance level to test whether this data contradicts the research report.

(a) State the null hypothesis and the alternate hypothesis. (Round your answers to 2 decimal places.)
H0: π =
H1: π ≠

(b) State the decision rule for 0.05 significance level. (Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places.)
H0 is rejected if z is not between _______ and _______

(c) Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

(d) Determine the p-value. (Round your answer to 4 decimal places.)

Two major automobile manufacturers have produced compact cars with the same size engines. We are interested in determining whether or not there is a significant difference in the MPG (miles per gallon) of the two brands of automobiles. A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance. The following data show the results of the test and if the variance of MPG is the same, Driver Manufacturer A Manufacturer B 1 32 28 2 27 22 3 26 27 4 26 24 5 25 24 6 29 25 7 31 28 8 27 27 Refer to Exhibit 6. The test statistic and the p-value at 99% confidence level are