The GPA of accounting students in a university is known to be normally distributed. A random sample of 32 accounting students results in a mean of 2.64 and a standard deviation of 0.15. Construct the 95% confidence interval for the mean GPA of all accounting students at this university.

Question 29 options: A researcher is studying the effectiveness of a new “brain training” game for Android phones, which the game’s developer says can improve memory. The game involves watching a series of cartoon animals run across the screen and tapping whenever the same animal appears twice. The researcher designs an experiment in which 20 participants (the memory group) play the game for 1 hour a day for a week. Another 20 participants (the non-memory group) plays a game with similar graphics but no memory demand for 1 hour a day for a week. At the end of the week, both groups complete a standardized memory test on their phone. Participants in the memory group had a mean standardized memory test score of 59.5338 with a standard deviation of 4.1700 and a SS of 330.3959. At the end of the week one of the participants in the non-memory group reports that he lost his phone at a bar over the St. Patrick’s day weekend and all his data are lost. For the remaining participants in the non-memory group, the mean score on the standardized memory task was 57.0333 with a standard deviation of 5.5714 and a SS of 558.7226. Conduct a hypothesis test at the alpha = 0.05 level? Fill in each of the blanks below. What type of test should you use (z-test; one sample t-test; independent samples t-test; or power analysis): Step 1: State the null hypothesis (just the null, no need to state the alternative; for μ1 simply type "mu1"): Step 2: what value defines the boundary of the positive critical region (enter a positive number with 5 decimal places using only the keys "0-9" and "."): Step 3: Calculate and then enter the observed value of the appropriate statistic (enter a number with 5 decimal places using only the keys "0-9" and "."): Step 4: Do you reject the null hypothesis (type yes or no): Finally, write one sentence to interpret the result of the hypothesis test in terms of the original research question (i.e., what does your result mean):

Assume the sample is taken from a normally distributed population. Construct 95​%

confidence intervals for​ (a) the population variance

σ^2

and​ (b) the population standard deviation

σ.

Interpret the results.

In a population of Siberian flying squirrels in western Finland, assume that the the number of pups born to each female over her lifetime has mean μ=3.66μ=3.66 and standard deviation σ=2.9598.σ=2.9598. The distribution of squirrel pups born is non‑normal because it takes only whole, non‑negative values.

Determine the mean number of pups, ¯¯¯¯¯X,X¯, such that in 90%90% of all random samples of such squirrels of size n=60,n=60, the mean number of pups born to females in the sample is less than ¯¯¯¯¯X.than X¯.

You may find the table of ZZ‑critical values useful.

Give your answer to at least two decimal places.

¯¯¯¯¯X=

2. (25p) You are about to take a 16-question true-false test. Assume you answer all 16 questions by guessing.
What is the probability of getting more than 10 questions correct?

3. (25p) A telephone number is selected at random from a directory. Suppose X denote the last digit of selected telephone number. Find the probability that the last digit of the selected number is
a. 5
b. less than 5
c. greater than or equal to 9

4. (25p) Suppose that the random variable Family income ~ N($65000, $320002). If the poverty level is $24,000, what percentage of the population lives in poverty?

6. Last year it was found that on average it took students 20 minutes to fill out the forms required for graduation. This year the department has changed the form and asked graduating student to report how much time it took them to complete the forms. Of the students 22 replied with their time, the average time that they reported was 18.5 minutes, and the sample standard deviation was 5.2. Can we conclude that the new forms take less time to complete than the older forms? Use a 0.1 significance level (i.e., p-value). (Assume that the reported times follow a Gaussian distribution)

Hand volume can be determined by measuring the amount of water displaced in a beaker after the hand is dipped in it. A student read a report that the median hand-volume of college-age males is 400ml. To test whether this is true at her school, she convinced 12 of her male friends to dip their hands in a beaker of water. Her measurements (in ml) are below:

400 360 420 520 460   350 500 420 450 430 395 400

1. Report the null and alternate hypotheses for a sign test
2. Report the number of positive and negative signs (remember this is based on a hypothesized median volume of 400 ml)
3. Report the P value and test statistic, do you accept or reject the null hypothesis?
4. Use a signed-rank test to re-run the analysis above.

You are working on a manufacturing process that should produce products that have a diameter of 3/4 of an inch. You take a random sample of 35 products and find the diameter to be 13/16 of an inch with a standard deviation of 5/32 of an inch. 1. Considering a t% level of significance, what can you state statistically about the process? Please include a null hypothesis, an alternative hypothesis, and use an appropriate test statistic (I.e. Zstat or Tstat).

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

A sample of 22 items provides a sample standard deviation of 5.

(a)Compute the 90% confidence interval estimate of the population variance. (Round your answers to two decimal places.)

(    ) to (    )

(b)Compute the 95% confidence interval estimate of the population variance. (Round your answers to two decimal places.)

( ) to (    )

(c) Compute the 95% confidence interval estimate of the population standard deviation. (Round your answers to one decimal place.)

(    ) to (    )

Archie has to go to school this morning for an important test, but he woke up late. He can either take the bus or take his unreliable car. If he takes the car, Archie knows from experience that he will make it to school without breaking down with probability 0.2. However, the bus to school runs late 65% of the time. Archie decides to choose between these options by tossing a coin. Suppose that Archie does, in fact, make it to the test on time. What is the probability that he took his car? Round your answer to two decimal places.

Consider the situation of this chapter, where we have to estimate the parameter N from a sample x1,...,xn drawn without replacement from the numbers {1,...,N}. To keep it simple, we consider n = 2. Let M = M2 be the maximum of X1 and X2. We have found that T2 = 3M/2 − 1 is a good unbiased estimator for N. We want to construct a new unbiased estimator T3 based on the minimum L of X1 and X2. In the following you may use that the random variable L has the same distribution as the random variable N + 1 − M (this follows from symmetry considerations). a. Show that T3 = 3L − 1 is an unbiased estimator for N. b. Compute Var(T3) using that Var(M)=(N + 1)(N − 2)/18. (The latter has been computed in Remark 20.1.) c. What is the relative efficiency of T2 with respect to T3?

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

Consider the following hypothesis test.

A sample of 75 is used and the population standard deviation is 10. Compute the p-value and state your conclusion for each of the following sample results. Use α = 0.01. (Round your test statistics to two decimal places and your p-values to four decimal places.)

(a) x = 23, Find the value of the test statistic.

?

Find the p-value.

p-value = ?

State your conclusion.

a) Reject H₀. There is sufficient evidence to conclude that μ ≠ 22.

b) Do not reject H₀. There is sufficient evidence to conclude that μ ≠ 22.    

c) Reject H₀. There is insufficient evidence to conclude that μ ≠ 22.

d) Do not reject H₀. There is insufficient evidence to conclude that μ ≠ 22.

(b) x = 25.1, Find the value of the test statistic.

?

Find the p-value.

p-value = ?

State your conclusion.

a) Reject H₀. There is sufficient evidence to conclude that μ ≠ 22.

b) Do not reject H₀. There is sufficient evidence to conclude that μ ≠ 22.    

c) Reject H₀. There is insufficient evidence to conclude that μ ≠ 22.

d) Do not reject H₀. There is insufficient evidence to conclude that μ ≠ 22.

(c)

x = 20

Find the value of the test statistic.

Find the p-value.

p-value =

State your conclusion.

Reject H₀. There is sufficient evidence to conclude that μ ≠ 22.Do not reject H₀. There is sufficient evidence to conclude that μ ≠ 22.    Reject H₀. There is insufficient evidence to conclude that μ ≠ 22.Do not reject H₀. There is insufficient evidence to conclude that μ ≠ 22.

The label on a 4-quart container of orange juice states that the orange juice contains an average of 1 gram of fat or less. Answer the following questions for a hypothesis test that could be used to test the claim on the label.

(a) Develop the appropriate null and alternative hypotheses.

a) H₀: μ = 1

b) H_a: μ ≠ 1

a) H₀: μ > 1

b) H_a: μ ≤ 1

a)H₀: μ ≥ 1

b) H_a: μ < 1

a) H₀: μ < 1

b) H_a: μ ≥ 1

a) H₀: μ ≤ 1

b) H_a: μ > 1

(b)What is the type I error in this situation? What are the consequences of making this error?

a) It is claiming μ < 1 when it is not. This error would claim that the product is not meeting its label specification when it really is meeting its specification.

b) It is claiming μ > 1 when it is not. This error would claim that the product is not meeting its label specification when it really is meeting its specification.   

c) It is claiming μ ≥ 1 when it is not. This error would miss the fact that the product is not meeting its label specification.

d) It is claiming μ ≤ 1 when it is not. This error would miss the fact that the product is not meeting its label specification.

(c) What is the type II error in this situation? What are the consequences of making this error?

a) It is concluding μ > 1 when it is not. This error would conclude that the product is not meeting its label specification when it really is meeting its specification.

b) It is concluding μ ≤ 1 when it is not. This error would miss the fact that the product is not meeting its label specification.   

c) It is concluding μ ≥ 1 when it is not. This error would miss the fact that the product is not meeting its label specification.

d) It is concluding μ < 1 when it is not. This error would conclude that the product is not meeting its label specification when it really is meeting its specification.

Suppose you own a publishing company. The daily production of books/magazines approximately follows normally distribution with a mean of 5,500 books/magazines per day with a standard deviation of 800 books/magazines per day.

A) Find 'a' such that, P(x>a) = 0.8997

B) Find 'a' such that, P(x<a) = 0.8888

Question 4: Consider a 28-3 fractional factorial design with design generators F=ABC, G=ABD, and H=BCDE

a) Find the complete defining relation and generate the alias structure using the principle (positive) fraction. Second, determine the design resolution (you need to show your justification).

b) List the basic variables and the design configuration (All 32 design points with the + and – signs. You should show the setting for all 8 factors by using the design generators) (Hint: Here there are 5 basic variables which you can use to generate the entire design)