The CPA Practice Advisor reports that the mean preparation fee for 2017 federal income tax returns was $273. Use this price as the population mean and assume the population standard deviation of preparation fees is $100.

A) What is the probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean?

B) What is the probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean?

C) What is the probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean?

D) Which, if any of the sample sizes in part (a), (b), and (c) would you recommend to ensure at least a .95 probability that the same mean is withing $16 of the population mean?

simple hypothesis test please be clear with algorithm

The United States and Japan often engage in intense trade negotiations. U.S. officials claim that Japanese manufacturers price their goods higher in Japan than in the United States, in effect subsidizing the low prices in the United States with extremely high prices in Japan. According to the U.S. argument, Japanese manufactures accomplish this by preventing U.S. good from reaching the market.

An economist decides to test the hypothesis that higher retail prices are being charged for automobiles in Japan than in the United States. She obtains independent samples from 50 retail sales in the United States and 50 sales in Japan over the same time. She found the sample average of the U.S. sales to be 26,596 and the sample average of the Japanese sales to be 27,236. The standard deviations were 1,981 and 1,974 respectively.

Using an alpha of 5%, conduct a hypothesis test.

Please solve clearly displaying the following:

What is the null hypothesis?

critical value?

What is the p-value?

declared alpha?

critical value?

Draw a conclusion?

Let X be a random variable representing the number of years of education an individual has, and let Y be a random variable representing an individual’s annual income. Suppose that the latest research in economics has concluded that:

Y = 6X +U

(1)

is the correct model for the relationship between X and Y , where U is another random variable that is independent of X. Suppose Var(X) = 2 and Var(Y ) = 172.

a. Find Var(U).

b. Find Cov(X, Y ) and corr(X, Y ).

c. The variance in Y (income) comes from variance in X (education) and U (other factors unobserved to us). What fraction of the variance in income is explained by variance in education?

d. How does the fraction you found in (c) compare to corr(Y, X)?

2. Let X be exponential with rate lambda. What is the pdf of Y = X^0.5? How about Y = X^3? Contrast the complexity of this result to transformation of a discrete random variable.

n a poker hand consisting of 5​ cards, find the probability of holding​ (a) 2 jacks​; ​(b) 1 diamond and 4 spades.

The management of a business concern will be making a decision whether to upgrade their office desktops to Windows 10 from Windows 7. However the management wants to see whether the employees are feeling comfortable in using Windows 10. A one-day training was organized on Windows 10, where all the personnel participated, of whom 20% are secretaries (A). After the seminar a survey was taken. It shows that among secretaries 55% want upgrade to Windows 10 (W10), 17% want no change from Windows 7 (W7), 28% have no preference (NP). Among non-secretarial employees the respective percentages are 39%, 55% and 6%.

If a personnel is selected at random, what is the probability that she is not a secretary, given that she made a definite preference? Answer to 3 digits after decimal.

1. A die is rolled twice. Find the joint probability mass function of X andY if X denotes the value on the first roll and Y denotes the minimum of the values of the two rolls.

A television sports commentator wants to estimate the proportion of citizens who​ "follow professional​ football." Complete parts​ (a) through​ (c). ​(a) What sample size should be obtained if he wants to be within 2 percentage points with 94​% confidence if he uses an estimate of 52​% obtained from a​ poll? The sample size is nothing. ​(Round up to the nearest​ integer.) ​(b) What sample size should be obtained if he wants to be within 2 percentage points with 94​% confidence if he does not use any prior​ estimates? The sample size is nothing. ​(Round up to the nearest​ integer.) ​(c) Why are the results from parts​ (a) and​ (b) so​ close? A. The results are close because 0.52 left parenthesis 1 minus 0.52 right parenthesis equals0.2496 is very close to 0.25. B. The results are close because the confidence 94​% is close to​ 100%. C. The results are close because the margin of error 2​% is less than​ 5%.

A statistics professor gave a 5-point quiz to the 50 students in his class. Scores on the quiz could range from 0 to 5: The following frequency table resulted: (1.5 points)

1. Compute the values that define the following percentiles:

a. 25^th   2     b. 50^th   3     c. 55^th   3    d. 75^th   4e. 80^th   4     f. 99^th    5    

2. What is the interquartile range of the data in #1?

3. Compute the exact percentile ranks that correspond to the following scores:

a. 2        b. 3        c. 4        d. 1   

Daily high temperatures in St. Louis for the last week were as​ follows: 92​, 94​, 93​, 95​, 95​, 86​, 95 ​(yesterday).

​a) The high temperature for today using a​ 3-day moving average ​= 92

degrees ​(round your response to one decimal​ place).

​b) The high temperature for today using a​ 2-day moving average ​= 90.5

degrees ​(round your response to one decimal​ place).

​c) The mean absolute deviation based on a​ 2-day moving average​ = 3.3

degrees ​(round your response to one decimal​ place).

​d) The mean squared error for the​ 2-day moving average​ = ____ degrees²???

​(round your response to one decimal​ place).

suppose that 65% of all registered voters in an area favor a certain policy. Among 225 randomly selected registered voters, find the following:

P(x ≤ 150)

, the probability that at most 150 favor the policy? Round to two decimal places.

P(x ≥ 140)

, the probability that at least 140 favor the the policy? Round to two decimal places.

3. A recent study showed that the average number of sticks of gum a person chews in a week is 15. A college student believes that the guys in his dormitory chew less gum in a week. He conducts a study and samples 14 of the guys in his dorm and finds that on average they chew 13 sticks of gum in a week with a standard deviation of 3.6. Test the college student's claim at αα=0.01.

Since the level of significance is 0.01 the critical value is -2.65

The test statistic is: (round to 3 places)

The p-value is: (round to 3 places)

4. A recent publication states that the average closing cost for purchasing a new home is $8859. A real estate agent believes the average closing cost is more than $8859. She selects 22 new home purchases and finds that the average closing costs are $8747 with a standard deviation of $107. Help her decide if she is correct by testing her claim at αα=0.05.

Since the level of significance is 0.05 the critical value is 1.721

The test statistic is: (round to 3 places)

The p-value is: (round to 3 places)

5. A new baker is trying to decide if he has an appropriate price set for his 3 tier wedding cakes which he sells for $81.85. He is particullarly interested in seeing if his wedding cakes sell for less than the average price. He searches online and finds that out of 43 of the competitors in his area they sell their 3 tier wedding cakes for $82.38. From a previous study he knows the standard deviation is $6.98. Help the new baker by testing this with a 0.01 level of significance.

Since the level of significance is 0.01 the critical value is 2.326

The test statistic is: (round to 3 places)

The p-value is: (round to 3 places)

A technician compares repair costs for two types of microwave ovens (type I and type II). He believes that the repair cost for type I ovens is greater than the repair cost for type II ovens. A sample of 60 type I ovens has a mean repair cost of $76.43$, with a standard deviation of $17.12. A sample of 46 type II ovens has a mean repair cost of $69.23, with a standard deviation of $19.14. Conduct a hypothesis test of the technician's claim at the 0.05 level of significance. Let μ1 be the true mean repair cost for type I ovens and μ2 be the true mean repair cost for type II ovens.

State the null and alternative hypotheses for the test.

Compute the value of the test statistic. Round your answer to two decimal places.

Determine the decision rule for rejecting the null hypothesis H0H0. Round the numerical portion of your answer to three decimal places.

Make the decision for the hypothesis test.

a) What is the probability that a hand of 13 cards contains four of a kind (e.g., four 5’s, four Kings, four aces, etc.)?

b) A single card is randomly drawn from a thoroughly shuffled deck of 52 cards. What is the probability that the drawn card will be either a diamond or a queen?

c) The probability that the events A and B both occur is 0.3. The individual probabilities of the events A and B are 0.7 and 0.5. What is the probability that neither event A nor event B occurs?

Suppose a bank quotes S = $1.1045/€. The annualized risk-free interest rates are 4% and 6% in the U.S and Germany, respectively. Find the approximate forward rate for the euro. Do not write any symbol. Make sure to round your answers to the nearest 100th decimal points. For example, write 1.2345 for $1.2345/€.

Suppose a bank quotes $/€ = 1.1045-1.1506. What is the bid-ask spread in percentage? Do not write any symbol. Express your answers as a percentage. Make sure to round your answers to the nearest 100th decimal points. For example, write 12.34 for 12.34%.