1. A new restaurant keeps track of the number of nightly customers at monthly intervals over the course of a year. The restaurant has done very little advertising; most of its publicity is by word of mouth but its number of customers is increasing. The restaurant does not have a seasonal difference in number of customers (for example, no summer crowds).

1. Using the data below, fit each an exponential regression model to the data using Excel.

1. Write down your regression equation.

2. Enter the regression equation into your calculator and use the table feature to estimate when the restaurant will have 400 people.

3. What does the model predict about the number of customers in 18 months?

4. What does the model predict as time goes on? For example how many customers will be at the restaurant in 300 months (25 years), is this reasonable?

5. What is the growth rate of your regression equation? Find and interpret it.

For finding p-values, there are two approaches - bootstrap or use a distribution for the test statistic under the null hypothesis (like standard normal, T, Chi-Square, F). Using the distribution approach requires some assumptions (such as normality, or approximate normality, of the population distribution, large sample sizes, etc.) For the following testing scenarios, write down the assumptions that are needed:

a. Testing of equality of proportions between two categorical variables - p1 and p2. Ho: p1 = p2 vs H1: p1 /= p2. Sample size n1 and n2

b. Testing for equality of proportions between three categorical variables using the Chi-Square Goodness of Fit approach Ho: p1 = p2 = p3 vs H1: at least one pair of pi's is not the same. Sample sizes n1, n2, n3. Total sample size n = n1+n2+n3

a. Testing of equality of population means between three populations using the ANOVA table. Ho: mu1 = m2 = mu3 vs H1: not all population means are the same Sample size n1, n2, n3

Marge owns three stocks: Apple, Google and Facebook. She expects the price per share of each stock one month from now to be 120, 60, and 60 dollars, respectively. An analysis of the returns to holding these three stocks shows that the monthly standard deviation of the price per share for each stock is 10, 8, and 8 dollars, respectively. This same analysis also concludes the covariance between the price per share of Apple stock and the price per share of Google stock is -36 (dollars squared), between Apple and Facebook it is +24, and between Google and Facebook it is +19. Assume Marge owns 200 shares of Apple, 100 shares of Google, and 50 shares of Facebook.

(a) Compute the expected value of Marge’s portfolio one month from now.

(b) Compute the standard deviation of the value of her portfolio one month from now.

(c) Marge’s sister, Maggie, owns 200 shares of Apple, 50 shares of Google, and 100 shares of Facebook. Who has the better portfolio? Explain and show any related work.

Question 8. For finding p-values, there are two approaches - bootstrap or use a distribution for the test statistic under the null hypothesis (like standard normal, T, Chi-Square, F). Using the distribution approach requires some assumptions (such as normality, or approximate normality, of the population distribution, large sample sizes, etc.)

For the following testing scenarios, write down the assumptions that are needed

a. Testing of equality of proportions between two categorical variables - p1 and p2.

Ho: p1 = p2 vs H1: p1 /= p2. Sample size n1 and n2

b. Testing for equality of proportions between three categorical variables using the Chi-Square Goodness of Fit approach

Ho: p1 = p2 = p3 vs H1: at least one pair of pi's is not the same. Sample sizes n1, n2, n3. Total sample size n = n1+n2+n3

a. Testing of equality of population means between three populations using the ANOVA table.

Ho: mu1 = m2 = mu3 vs H1: not all population means are the same Sample size n1, n2, n3

Time spent using​ e-mail per session is normally​ distributed, with mu equals 8 minutes and sigma equals 2 minutes. Complete parts​ (a) through​ (d).

a. If you select a random sample of 25 ​sessions, what is the probability that the sample mean is between 7.8 and 8.2 ​minutes?

=0.3830 ​(Round to three decimal places as​ needed.)

b. If you select a random sample of 25 ​sessions, what is the probability that the sample mean is between 7.5 and 8 ​minutes?

= 0.3944 ​(Round to three decimal places as​ needed.)

c. If you select a random sample of 200 ​sessions, what is the probability that the sample mean is between 7.8 and 8.2 ​minutes? ​

d. Explain the difference in the results of​ (a) and​ (c). Choose the correct answer below. The sample size in​ (c) is greater than the sample size in​ (a), so the standard error of the mean​ (or the standard deviation of the sampling​ distribution) in​ (c) is ......... than in​ (a). In​ general, as the standard deviation​ decreases, values become ........ concentrated around the mean.​ Therefore, the probability of a region that includes the mean will always ........ when the sample size increases.

Python program

A number game machine consists of three rotating disks labelled with the numbers 0 to 9 (inclusive). If certain combinations of numbers appear when the disks stop moving, the player wins the game.

The player wins if

• the first and third numbers are the same, and the second number is less than 5, or
• all three numbers are the same, or
• the sum of the first two numbers is greater than the third number;

otherwise the player loses.

Write a Python program to simulate this number game by randomly generating 3 integer values between 0 and 9 (inclusive), and printing whether the player has won or lost the game.

To randomly generate a number between and including 0 and 9, use the randintmethod from random library module. For example, x = random.randint(1,100)will automatically generate a random integer between 1 and 100 (inclusive) and store it in x.

Sample output 1:

Random numbers: 2 3 5
You lose.

Sample output 2:

Random numbers: 7 7 0
You win!

Drosophila has three linked autosomal genes that determine different traits. These genes are black (b), vestigial (vg), and singed(sn). Each of the three genes has two alleles: a dominant wild type allele, indicated by a "+" (plus) and a recessive mutant allele indicated by a "-" (minus). (These mutant alleles cause dark black spots, short "vestigial" wings, and bent "singed" hairs, respectively, when homozygous). A testcross is conducted between females that all have the same genotype and are triple heterozygotes for the three genes, and males that are all homozygous mutant for all three genes. Here are the numbers of progeny from the testcross, of each of the different possible phenotypes:

Progeny
Group     Phenotype       Number

   1 b+ vg - sn- 638

   2 b+ vg + sn- 2768

   3 b- vg + sn+ 621

   4 b+ vg + sn+ 9

   5 b+ vg-   sn+ 126

   6 b-   vg -   sn- 7

   7 b- vg + sn- 132

   8 b- vg - sn+ 2699

Total # progeny = 7000

In the answer box below, give your answers to parts A and B.

A. From the data above, determine the genotype of the triple heterozygous females used in the testcross; in your genotype, be sure to include the proper order of the genes on the chromosomes. Indicate the genotype with a slash between the two homologous chromosomes (8 points)

(Example of format for an answer: a+ b- c- / a- b+ c+
but use b, vg and sn instead of a, b and c, and put them in the correct order with the correct + and - alleles on the same homologue)

B. Type in three equations, numbered 1, 2, and 3. each with the proper numbers for calculating the genetic distances between the genes indicated (You do not need to complete the calculation.) (6 points)

1. black (b) and vestigial (vg)

2. vestigial (vg) and singed (sn)

3. black (b) and singed (sn)

Format for each answer: For example, if to determine the distance for #1, between black and vestigial, you think you should add the progeny in group 4 and the progeny in group 5 and divide by the total number of progeny, type this as your answer:
1. 9+126/7000 (Of course, this is not the correct answer for #1!)

We wish to compare the PsyCap scores of our class to a predetermined standard set by a study conducted in 2014. The population mean for this standard is 121. 58 with a standard deviation of 11.29.  

Utilizing the steps of hypothesis testing, determine if the scores of our class are equal to those of the standard using a 95% confidence level.

Answer

Step 1

Our Hypothesis

Ho: Ho =   μ = 121.58 (equal to(null))

Ha: μ ≠ 121.58 (not equal to (alternative))

Step 2

Specify the significance level a(alpha)

a = 0.05

Step 3   (also step 5)

Select the test statistic (two tailed test, this means two rejecting regions)

     (103.76-121.58)/ 11.29/ square root of 17 = -6.507

                                   0.95

0.025                                                                0.025

               -1.96                                      1.96

Step 4

The rule is to decide whether the z equals that of Ho, if it is less or more we reject and favor the alternative Ha

Step 5

     (103.76-121.58)/ 11.29/ square root of 17 = -6.507

                                   0.95

0.025                                                                0.025

               -1.96                                      1.96

Step 6 Decide whether to reject Ho

Because the result was -6.507, we choose to reject Ho

Step 7

We conclude that scores are below 2014’s data, meaning it is not equal.

A vehicle quality survey asked new owners a variety of questions about their recently purchased automobile. One question asked for the owner’s rating of the vehicle using categorical responses of average, outstanding, and exceptional. Another question asked for the owner’s education level with the categorical responses some high school, high school graduate, some college, and college graduate. The Excel Online file below contains the sample data for 500 owners who had recently purchased an automobile. Construct a spreadsheet to answer the following questions.

Observed Frequency Table

Expected Frequency Table

a. Use a .05 level of significance and a test of independence to determine if a new owner's vehicle quality rating is independent of the owner's education.

Compute the value of the  test statistic (to 2 decimals).

???????

The p-value is ????? (to 4 decimals).

What is your conclusion?

Cannot conclude that the quality rating is not independent of the education of the owner.

b. Use the overall percentage of average, outstanding, and exceptional ratings to comment upon how new owners rate the quality of their recently purchased automobiles.

Average: 27% (to whole number)

Outstanding: 47% (to whole number)

Exceptional: 26% (to whole number)

New owners appear to be satisfied with the recent purchase of their automobile. 73% (to whole number) of owners rated their automobile as Outstanding or Exceptional.

ASAP due tonight!