Show algebraically that E(Var(β1hat)) = σ^2/(n-1)σ_x²

QUESTION 6 Using Table A, p.690-691, the area to the right of the z score 0.52 would be a. 0.52 b. 0.6985 c. 0.3015 d. -0.52

QUESTION 7 The data point 91 is taken from a normal distribution that has a mean of 75 and a standard deviation of 8. What is the z-score of the data point? Round to the nearest hundredth.

QUESTION 8 A data point is taken from a normal distribution that has a mean of 15.4 and a standard deviation of 0.25. If the z-score of the data point is -1, then what is the value of the data point? Round to the nearest tenth

QUESTION 9 A normal distribution for weights of filled cereal boxes has a mean of 17.98 ounces and a standard deviation of 0.1144 ounces. What is the z-score for the weight of 17.91 ounces? Round to the nearest hundredth

QUESTION 10 A data point is taken from a normal distribution that has a mean of 99 and a standard deviation of 0.4. If the z-score of the data point is 2.57, then what is the value of the data point? Round to the nearest hundredth.

QUESTION 11 Use your TI83 (or Excel): A normally distributed population has a mean of 77 and a standard deviation of 15. Determine the probability that a random data has a value of less than 74. Round to four decimal places.

QUESTION 12 Use your TI83 (or Excel): A normally distributed population has a mean of 77 and a standard deviation of 12. Determine the probability that a random data has a value between 72 and 80. Round to four decimal places.

QUESTION 13 Use your TI83 (or Excel): A normally distributed population has a mean of 74 and a standard deviation of 18. Determine the probability that a random data has a value between 71 and 82. Round to four decimal places.

QUESTION 14 Use your TI83 (or Excel): A normally distributed population has a mean of 72 and a standard deviation of 20. Determine the probability that a random data has a value between 74 and 81. Round to four decimal places.

QUESTION 15 Use your TI83 (or Excel): A normally distributed population has a mean of 79 and a standard deviation of 14. Determine the probability that a random data has a value of less than 77. Round to four decimal places.

You’ve been asked to carry out a quantitative analysis of your company’s marketing campaign, and have been given permission to gather all the data you believe necessary. Drawing on all the material covered what strategies will you employ to carry out this task? Identify the variables you would collect and the types of statistical analyses you would use.

PLEASE WRITE CLEAR!

Let x represent the dollar amount spent on supermarket impulse buying in a 10-minute (unplanned) shopping interval. Based on a certain article, the mean of the x distribution is about $31 and the estimated standard deviation is about $8. (a) Consider a random sample of n = 70 customers, each of whom has 10 minutes of unplanned shopping time in a supermarket. From the central limit theorem, what can you say about the probability distribution of x, the average amount spent by these customers due to impulse buying? What are the mean and standard deviation of the x distribution? The sampling distribution of x is not normal. The sampling distribution of x is approximately normal with mean μx = 31 and standard error σx = $0.11. The sampling distribution of x is approximately normal with mean μx = 31 and standard error σx = $8. The sampling distribution of x is approximately normal with mean μx = 31 and standard error σx = $0.96. Is it necessary to make any assumption about the x distribution? Explain your answer. It is not necessary to make any assumption about the x distribution because μ is large. It is necessary to assume that x has a large distribution. It is necessary to assume that x has an approximately normal distribution. It is not necessary to make any assumption about the x distribution because n is large. (b) What is the probability that x is between $29 and $33? (Round your answer to four decimal places.) (c) Let us assume that x has a distribution that is approximately normal. What is the probability that x is between $29 and $33? (Round your answer to four decimal places.) (d) In part (b), we used x, the average amount spent, computed for 70 customers. In part (c), we used x, the amount spent by only one customer. The answers to parts (b) and (c) are very different. Why would this happen? The standard deviation is smaller for the x distribution than it is for the x distribution. The x distribution is approximately normal while the x distribution is not normal. The sample size is smaller for the x distribution than it is for the x distribution. The mean is larger for the x distribution than it is for the x distribution. The standard deviation is larger for the x distribution than it is for the x distribution. In this example, x is a much more predictable or reliable statistic than x. Consider that almost all marketing strategies and sales pitches are designed for the average customer and not the individual customer. How does the central limit theorem tell us that the average customer is much more predictable than the individual customer? The central limit theorem tells us that small sample sizes have small standard deviations on average. Thus, the average customer is more predictable than the individual customer. The central limit theorem tells us that the standard deviation of the sample mean is much smaller than the population standard deviation. Thus, the average customer is more predictable than the individual customer.

Suppose we wish to generate a sample from the exponential ($\beta$) distribution, and only have access to a computer which generates numbers from the skew logistic distribution. It turns out that if $X$~SkewLogistic ($\beta$), then log(1+exp($-X$)) is exponential ($\beta$). Show that this is true and check by simulation that this transformation is correct.

The table below gives the age and bone density for five randomly selected women. Using this data, consider the equation of the regression line, yˆ=b0+b1xy^=b0+b1x, for predicting a woman's bone density based on her age. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant.

Step 4 of 6:

Substitute the values you found in steps 1 and 2 into the equation for the regression line to find the estimated linear model. According to this model, if the value of the independent variable is increased by one unit, then find the change in the dependent variable yˆy^.

Step 6 of 6:

Find the value of the coefficient of determination. Round your answer to three decimal places.

1. On average, do hospitals in the United States employ fewer than 900 personnel? Use the hospital database as your sample and an alpha of 0.10 to test this figure as the alternative hypothesis. Assume that the number of births and number of employees in the hospitals are normally distributed in the population.

2. Personnel
   792
   1762
   2310
   328
   181
   1077
   742
   131
   1594
   233
   241
   203
   325
   676
   347
   79
   505
   1543
   755
   959
   325
   954
   1091
   671
   300
   753
   607
   929
   354
   408
   1251
   386
   144
   2047
   1343
   1723
   96
   529
   3694
   1042
   1071
   1525
   1983
   670
   1653
   167
   793
   841
   316
   93
   373
   263
   943
   605
   596
   1165
   568
   507
   479
   136
   1456
   3486
   885
   243
   1001
   3301
   337
   1193
   1161
   322
   185
   205
   1224
   1704
   815
   712
   156
   1769
   875
   790
   308
   70
   494
   111
   1618
   244
   525
   472
   94
   297
   847
   234
   401
   3928
   198
   1231
   545
   663
   820
   2581
   1298
   126
   2534
   251
   85
   432
   864
   66
   556
   347
   239
   973
   439
   1849
   102
   262
   885
   549
   611
   330
   1471
   75
   262
   328
   377
   575
   1916
   2620
   571
   703
   535
   160
   202
   1330
   370
   3123
   2745
   815
   576
   502
   808
   50
   728
   4087
   3012
   68
   3090
   1358
   576
   284
   145
   2312
   1124
   336
   415
   1779
   338
   453
   437
   261
   609
   647
   61
   2074
   2232
   948
   409
   153
   741
   1625
   538
   789
   395
   956
   362
   144
   229
   396
   2256
   731
   1477
   102
   106
   939
   392
   3516
   785
   607
   273
   630
   1379
   1108
   583
   514
   216
   1593
   1055
   399
   834
   104

Sheila's doctor is concerned that she may suffer from gestational diabetes (high blood glucose levels during pregnancy). There is variation both in the actual glucose level and in the blood test that measures the level. A patient is classified as having gestational diabetes if the glucose level is above 140 milligrams per deciliter (mg/dl) one hour after a sugary drink is ingested. Sheila's measured glucose level one hour after ingesting the sugary drink varies according to the Normal distribution with μ = 124 mg/dl and σ = 10 mg/dl. What is the level L such that there is probability only 0.05 that the mean glucose level of 2 test results falls above L for Sheila's glucose level distribution? (Round your answer to one decimal place.)

The following data represent the weight​ (in grams) of a random sample of 13 medicine tablets. Find the​ five-number summary, and construct a boxplot for the data. Comment on the shape of the distribution.

0.600 0.598 0.598 0.600 0.600 0.599 0.604 0.611 0.606 0.599 0.601 0.602 0.604  

find the five number summary

The weight of an organ in adult males has a​ bell-shaped distribution with a mean of 310 grams and a standard deviation of 20 grams. Use the empirical rule to determine the following.

​(a) About 95​% of organs will be between what​ weights?

​(b) What percentage of organs weighs between 250 grams and 370 grams?

​(c) What percentage of organs weighs less than 250 grams or more than 370 ​grams?

​(d) What percentage of organs weighs between 250 grams and 330 grams?

Price change to maximize profit. A business sells n products, and is considering changing the price of one of the products to increase its total profits. A business analyst develops a regression model that (reasonably accurately) predicts the total profit when the product prices are changed, given by Pˆ = βT x + P , where the n-vector x denotes the fractional change in the product prices, xi = (pnew − pi)/pi. Here P is the profit with the currentiprices, Pˆ is the predicted profit with the changed prices, pi is the current (positive) price of product i, and pnew is the new price of product i.

1. (a) What does it mean if β3 < 0? (And yes, this can occur.)

2. (b) Suppose that you are given permission to change the price of one product, by up to 1%, to increase total profit. Which product would you choose, and would you increase or decrease the price? By how much?

3. (c) Repeat part (b) assuming you are allowed to change the price of two products, each by up to 1%.

Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us.

(a) Suppose n = 34 and p = 0.33.

(For each answer, enter a number. Use 2 decimal places.)
n·p =
n·q =

Can we approximate p̂ by a normal distribution? Why? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)

_____, p̂ _____ be approximated by a normal random variable because _____ _____.

first blank

Yes/No    

second blank

can/cannot    

third blank

both n·p and n·q exceed

n·q exceeds

n·p exceeds

n·q does not exceed

n·p and n·q do not exceed

n·p does not exceed

fourth blank (Enter an exact number.)


What are the values of μ_p̂ and σ_p̂? (For each answer, enter a number. Use 3 decimal places.)
μ_p̂ = mu sub p hat =
σ_p̂ = sigma sub p hat =

(b)

Suppose n = 25 and​​​​​​​ p = 0.15. Can we safely approximate p̂ by a normal distribution? Why or why not? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)

_____, p̂ _____ be approximated by a normal random variable because _____ _____.

first blank

Yes/No    

second blank

can/cannot    

third blank

both n·p and n·q exceed

n·q exceeds

n·p exceeds

n·q does not exceed

n·p and n·q do not exceed

n·p does not exceed

fourth blank (Enter an exact number.)

(c) Suppose n = 52 andcp = 0.22.

(For each answer, enter a number. Use 2 decimal places.)
n·p =
n·q =

Can we approximate p̂ by a normal distribution? Why? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)

_____, p̂ _____ be approximated by a normal random variable because _____ _____.

first blank

Yes/No    

second blank

can/cannot    

third blank

both n·p and n·q exceed

n·q exceeds

n·p exceeds

n·q does not exceed

n·p and n·q do not exceed

n·p does not exceed

fourth blank (Enter an exact number.)


What are the values of μ_p̂ and σ_p̂? (For each answer, enter a number. Use 3 decimal places.)
μ_p̂ = mu sub p hat =

σ_p̂ = sigma sub p hat =

A die is tossed once, and the face, n, is noted. Then an integer m is selected at random from the set {1,2,···,n}, which depends on the face n. a). Find the probability that m = 3. b). Given that m = 3, what is the probability that n = 6?