You started taking the bus to work. The local transit authority says that a bus should arrive at your bus stop every five minutes. After a while, you notice you spend a lot more than five minutes waiting for the bus, so you start to keep a record.

You spend the next two months recording how long it takes for the bus to arrive to the bus stop. This give a total of sixty observations that denote the number of minutes it took for the bus to arrive (rounded to the nearest minute). These observations are hosted at

   https://mattbutner.github.io/data/bus_stop_time.csv

Load these data into R as a data frame titled bus_stop_time

Create a histogram of the time_until_bus varaible. Would you say that five minutes is a reasonable guess for the average arrival time based on this picture alone?

Create 95% confidence interval for the bus arrival times using the Z distribution. Does 5 minutes fall within the 95% confidence interval?

How would you communicate your finding to the local transit authority?

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

In a random sample of 63 professional actors, it was found that 39 were extroverts.

(a) Let p represent the proportion of all actors who are extroverts. Find a point estimate for p. (Round your answer to four decimal places.)


(b) Find a 95% confidence interval for p. (Round your answers to two decimal places.)

Give a brief interpretation of the meaning of the confidence interval you have found.

We are 5% confident that the true proportion of actors who are extroverts falls within this interval.We are 95% confident that the true proportion of actors who are extroverts falls outside this interval.    We are 5% confident that the true proportion of actors who are extroverts falls above this interval.We are 95% confident that the true proportion of actors who are extroverts falls within this interval.

(c) Do you think the conditions np > 5 and nq > 5 are satisfied in this problem? Explain why this would be an important consideration.

Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately binomial.No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately normal.    Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately normal.No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately binomial.

A study  examined whether or not noses continue to grow throughout a person’s lifetime.  The study included many measurements (including size of the nose as measured by total volume) and included multiple tests.  For each of the tests described below:

            a)  State the null and alternative hypotheses.

            b) Give a formal decision using a 5% significance level, and interpret the conclusion in context.

• In a test to see whether males, on average, have bigger noses than females, the study indicates that “p < 0.01.”
• In a test to see whether there is a positive linear relationship between age and nose size, the study indicates that “p < 0.001.”

The failure rate in a statistics class is 20%. In a class of 30 students, find the probability that exactly five students will fail. Use the normal distribution to approximate the binomial distribution.

The mean number of pets per household is 2.96 with standard deviation 1.4. A sample of 52 households is drawn. Find the probability that the sample mean is less than 3.11.

The pH of 20 randomly selected lakes is measured. Their average pH is 5.7.

Part A. Historically the standard deviation in the pH values is 0.9. Use this standard deviation for the following questions.
Part Ai. Build a 95% confidence interval for the population mean lake pH.
Part Aii. Build a 90% confidence interval for the population mean lake pH.
Part Aiii. Build an 80% confidence interval for the population mean lake pH.
Part Aiv. Compare the intervals you created in Ai, Aii and Aiii. What effect does changing the level of confidence have on the interval?

Please solve only part B

Part B. For the 20 measured lakes the standard deviation in the pH values is 0.9. Use this standard deviation for the following questions.
Part Bi. Build a 95% confidence interval for the population mean lake pH.
Part Bii. Compare the confidence intervals in Bi and Ai. What effect does not knowing the value of ? have on the interval?
Part Biii. Test whether the population mean pH differs from 6.

For 300 trading​ days, the daily closing price of a stock​ (in $) is well modeled by a Normal model with a mean of

​$197.12197.12 and a standard deviation of

​$7.187.18. According to this​ model, what is the probability that on a randomly selected day in this​ period, the stock price closed as follows.

​a) above ​$204.30204.30​?

​b) below ​$211.48211.48​?

​c) between ​$182.76182.76 and ​$211.48211.48​?

Hale's TV Productions is considering producing a pilot for a comedy series in the hope of selling it to a major television network. The network may decide to reject the series, but it may also decide to purchase the rights to the series for either one or two years. At this point in time, Hale may either produce the pilot and wait for the network's decision or transfer the rights for the pilot and series to a competitor for $250,000. Hale's decision alternatives and profits (in thousands of dollars) are as follows:

The probabilities for the states of nature are P(S₁) = 0.20, P(S₂) = 0.30, and P(S₃) = 0.50. For a consulting fee of $45,000, an agency will review the plans for the comedy series and indicate the overall chances of a favorable network reaction to the series. Assume that the agency review will result in a favorable (F) or an unfavorable (U) review and that the following probabilities are relevant:

a. What is the expected value?

b. What is the expected value of perfect information?

c. What is the expected value of the agency's information? Round your answer to two decimal places.

d. What is the maximum that Hale should be willing to pay for the information? Round your answer to two decimal places.

In each of parts​ (a)-(c), we have given a likely range for the observed value of a sample proportion p. Based on the given​ range, identify the educated guess that should be used for the observed value of p to calculate the required sample size for a prescribed confidence level and margin of error.

a. 0.2 to 0.3

b. 0.1 or less

c. 0.3 or greater

Physical activity of obese young adults. In a study on the physical activity of young adults, pediatric researchers measured overall physical activity as the total number of registered movements (counts) over a period of time and then computed the number of counts per minute (cpm) for each subject (International Journal of Obesity, Jan. 2007). The study revealed that the overall physical activity of obese young adults has a mean of μ = 320 cpm μ = 320   cpm and a standard deviation of σ = 100 c p m . σ = 100 c p m . (In comparison, the mean for young adults of normal weight is 540 cpm.) In a random sample of n = 100 n = 100 obese young adults, consider the sample mean counts per minute, ¯ x x ‾ . Describe the sampling distribution of ¯ x x ‾ . What is the probability that the mean overall physical activity level of the sample is between 300 and 310 cpm? What is the probability that the mean overall physical activity level of the sample is greater than 360 cpm?

Please Double Check answers I've recived 3 wrong answers on three diffrent questions today thank you

CNNBC recently reported that the mean annual cost of auto insurance is 1006 dollars. Assume the standard deviation is 245 dollars. You take a simple random sample of 73 auto insurance policies.

Find the probability that a single randomly selected value is less than 973 dollars. P(X < 973) =

Find the probability that a sample of size n = 73 is randomly selected with a mean less than 973 dollars. P(M < 973) =

A sample containing years to maturity and yield for 40 corporate bonds are contained in the data given below.

a. What is the sample mean years to maturity for corporate bonds and what is the sample standard deviation?

b. Develop a 95% confidence interval for the population mean years to maturity. Round the answer to four decimal places.

（ , ） years

c. What is the sample mean yield on corporate bonds and what is the sample standard deviation?

d. Develop a 95% confidence interval for the population mean yield on corporate bonds. Round the answer to four decimal places.

（ , ）percent

As a data scientist of a company, you want to analyze the following data collected by your company which relates the advertising expenditure A in thousands of dollars to total sales S in thousands of dollars. The following table shows this relationship

Using Advertising expenditure (A) as the domain and Total Sales (S) as the range, the data is not a function because the value 18.8 and 19 appear in the domain more than once with a different corresponding value of the range each time.

--Interpret the slope and y-intercept of this equation.

--Express this equation as a function S of A and find its domain.

--Predict the sales if the advertising expenditure is $25000.