In a certain distribution of​ numbers, the mean is 60​, with a standard deviation of 5. Use​ Chebyshev's Theorem to tell what percent of the numbers are less than 50 or more than 70.  

1. The sandwich company, Alamo Lone Star (ALS) prepares sandwiches for sale in vending machines in a large number of locations in an urban area. The four types of sandwich that are now provided are those that have been found to sell well. The following information is available on each type:

The most popular sandwich is the cheese and salad so ALS ensure that at least half of all sandwiches supplied are cheese and salad. All four types of sandwich are prepared each evening and then distributed to the vending machines the next morning. Sandwich preparation is carried out by five part-time workers. Four of these workers each work 3.5 hours each evening and one works for only two hours. KLS has 50 identical sandwich vending machines each with a capacity of 40 units.

The manager of ALS needs to know how many of each type of sandwich they should produce each evening in order to maximize profit subject to unit profit figures and constraints mentioned above.

This problem was formulated as a linear programming model and then solved using Excel Solver. The Excel Solver output is provided in the appendix.

Using the Solver output and where necessary the information given above, answer the following questions (include with your answers brief explanations). In each part of the question you must assume that any changes considered in any earlier part of the question have not been implemented.

Please note that to keep the model as simple as possible, it was assumed that ALS can sell all sandwiches they produced.

Refer to above Excel output, ALS has concerns about their supplier of ham and has decided to switch to a new supplier. Because of this switch, for just one day they will not be able to supply any ham and cheese sandwiches. What would happen to the total daily profit?

How many of each type of sandwich should ALS produce each evening in order to maximize profit and what will this profit be?

An economist would recommend that the Bank of Canada change the interest rate for borrowed money if the average annual inflation rate is less than 2.15%. Based on a sample from the past 21 years, the average annual inflation rate was 1.87%, with a standard deviation of 0.67%. Assume the population is approximately normally distributed.

(a) [1 mark] Define the parameter you are testing.

(b) [1 mark] State the null hypothesis and alternative hypothesis you would use to test whether there was sufficient evidence that the average annual inflation rate was less than 2.15%.

(c) [1 mark] Assuming that H0 is true, what is the formula for the appropriate test statistic? How is it distributed? If it is t-distributed, be sure to indicate the number of degrees of freedom.

(d) [1 mark] Compute the observed value of the test statistic.

(e) [2 marks] Determine the p-value to within table accuracy. If your test statistic is zdistributed, this will be an exact value; if your test statistic is t-distributed, indicate the tightest possible bounds on the p-value.

(f) [1 mark] Report the strength of the evidence against H0 in favour of H1.

(g) [1 mark] Report the estimated value of the parameter and the estimated standard error.

(h) [2 marks] Would you reject your null hypothesis H0 when using a significance level of α = 0.01? Write a concluding sentence about the economist’s decision regarding the mean annual inflation rate.

In what follows use any of the following tests: Regression, multiple regression, one-sided t-test, or two-sided t-test. All conclusions should be based on 5% P-value threshold.

Choose the best fitting answer.

Open Brains data. SETUP: Since females are on average smaller than males, some people believe that female brains should be smaller as well (smaller volume). Given the data, your job is to perform the appropriate statistical test or procedure and help them decide.

5. What test did you perform?

• a. Regression
• b. ​​Multiple regression
• c. One-sided t-test
• d. ​​Two-sided t-test

6. What is the P-value?

• a. 0.115912154
• b. 0.057956077
• c. 7.38553E-20
• d. 3.69277E-20
• e. None of these

7. What is the Statistical interpretation?

• a. Since P-value is very small we can conclude that female brain is smaller in volume.
• b. Since P-value is too large we cannot conclude that male and female brains have different volume.
• c. Since P-value is too large we cannot conclude that female brain is smaller in volume.
• d. None of these.

8. What is the conclusion?

• a. Test is inconclusive; thus nothing can be concluded.
• b. Test is inconclusive; thus we cannot claim that the brain volumes are different.
• c. Test is inconclusive; thus we cannot claim that there is a correlation between brain volume and gender.
• d. None of these.

CCMIDSA: Corpus Collasum Surface Area (cm2)   FIQ: Full-Scale IQ   HC: Head Circumference (cm)   ORDER: Birth Order   PAIR: Pair ID (Genotype)   SEX: Sex (1=Male 2=Female)   TOTSA: Total Surface Area (cm2)   TOTVOL: Total Brain Volume (cm3)   WEIGHT: Body Weight (kg)
8.42   96   57.2   1   6   1   1806.31   1079   61.236
7.44   88   57.2   1   7   1   2018.92   1104   79.38
6.84   85   57.2   1   8   1   2154.67   1439   99.792
6.48   97   57.2   1   9   1   1767.56   1029   81.648
6.43   124   58.5   1   10   1   1971.63   1160   72.576
7.62   101   57.2   2   6   1   1689.6   1173   61.236
6.03   93   57.2   2   7   1   2136.37   1067   83.916
6.59   94   55.8   2   8   1   1966.81   1347   97.524
7.52   114   56.5   2   9   1   1827.92   1100   88.452
7.67   113   59.2   2   10   1   1773.83   1204   79.38
6.08   96   54.7   1   1   2   1913.88   1005   57.607
5.73   87   53   1   2   2   1902.36   1035   64.184
6.22   101   57.8   1   3   2   2264.25   1281   63.958
5.8   103   56.6   1   4   2   1866.99   1051   133.358
7.99   127   53.1   1   5   2   1743.04   1034   62.143
7.99   89   54.2   2   1   2   1684.89   963   58.968
8.76   87   52.9   2   2   2   1860.24   1027   58.514
6.32   103   56.9   2   3   2   2216.4   1272   61.69
6.32   96   55.3   2   4   2   1850.64   1079   107.503
7.6   126   54.8   2   5   2   1709.3   1070   83.009

final exam scores in a mathematics course are normally distributed with a mean of 79 and a standard deviation of 8. an exam score is 103 and the Z score is 3, what is the percentile

What are the requirements for a probability distribution? Differentiate between a discrete and a continuous random variable. Discuss the requirements for a binomial probability experiment.

An important part of employee compensation is a benefits package, which might include health insurance, life insurance, child care, vacation days, retirement plan, parental leave, bonuses, etc. Suppose you want to conduct a survey of benefits packages available in private businesses in Hawaii. You want a sample size of 100.

Some sampling techniques are described below. Categorize each technique as simple random sample, stratified sample, systematic sample, cluster sample, or convenience sample. Put your answer in the blank.

a. Assign each business in the Island Business Directory a number, and then use a random number table to select the businesses to be included in the sample. __________________________

b. Use postal ZIP Codes to divide the state into regions. Pick a random sample of 10 ZIP Code areas and then include all the businesses in each selected ZIP Code area. ________________________

c. Send a team of five research assistants to Bishop Street in downtown Honolulu. Let each assistant select a block or building and interview an employee from each business found. Each researcher can have the rest of the day off after getting responses from 20 different businesses. _____________________

d. Use the Island Business Directory. Number all the businesses. Select a starting place at random, and then use every 50th business listed until you have 100 businesses. _____________________

e. Group the businesses according to type: medical, shipping, retail, manufacturing, financial, construction, restaurant, hotel, tourism, other. Then select a random sample of businesses from each business type. ____________________

The Accountability ratings for sixteen (16) school districts in the Delta Region of Mississippi on a 500 point rating scale are as follows: 302, 125, 225, 279, 108, 420, 350, 149, 129, 382, 114, 141, 180, 209, 156, & 163

Determine the following:

a. Third Decile

b. Fourth Decile

c. Fifth Decile

d. Sixth Dealle

e. Seventh Decile

f. Eighth Decile

g. Ninth Decile

***Please explain

1) The World Health Organization (WHO) studied the woman’s life expectancy and associated risk factors. They found a linear relationship as: Life expectancy (year) = 47.17 + 30.7 Literacy percentage among women. Based on this linear model, what is the woman’s life expectancy in Mexico when women’s literacy percentage is about 80%?   

• 77.87 years old

• 76.77 years old

• Around 81 years old

• 71.73 years old

2) Study investigators at the University of Florida wanted to evaluate the correlation of mean admission multiple mini-interview (MMI) scores with cumulative (continuous data) and overall GPA across didactic years 1-3 in the doctor of pharmacy program. Which of the following should be used to calculate the correlation coefficient?  

• Pearson correlation

• Spearman correlation

• Kendall correlation  

• Canonical correlation

3) The results of the study are shown in Table 2 below. Which of the following statements is CORRECT?

Table Information: Mean Cumulative GPA= 3.61

Mean MMI Score (Max 24)= 19

Correlation Coefficient (r)= -0.05

p value=0.29

R^2= 0.003

• There was NOstatistically significant correlation between MMI score and GPA.

• There was a statistically significant negative correlation between MMI score and GPA.

• The mean MMI score in the regression model accounted for 0.003% of the total variation in a given student’s cumulative GPA.

• There was moderate negative correlation between MMI score and GPA.

4) Look at Table 2 below. Which independent variable had the largest contribution to the total PCOA score? (clue: β is the standardized coefficient in the Table.)

• PCAT Score  

• PY3 Pre-APPE GPA  

• NAPLEX Score

• R2

Use the information below to answer questions 11-15. A random sample of 1000 voters registered in the state of Montana showed that 490 voted in the last general election. A random sample of 800 voters in the state of Arizona showed that 368 voted in the most recent general election. Do these data indicate that the population percentage of voter turnout in Arizona is lower than that in Montana? 11. Choose the appropriate null and alternate hypotheses. a. Null: The percentage of people who voted in Arizona and Montana is the same Alternate: The percentage of people who voted in Arizona is more than in Montana b. Null: The percentage of people who voted in Arizona is more than in Montana Alternate: The percentage of people who voted in Arizona and Montana is the same c. Null: The percentage of people who voted in Arizona and Montana is the same Alternate: The percentage of people who voted in Arizona is less than in Montana d. Null: : The percentage of people who voted in Arizona is less than in Montana Alternate: The percentage of people who voted in Arizona and Montana is the same 12. What is the standard error for the difference (SEdiff)? a. 0.03% b. 0.71% c. 3.0% d. 2.37% 13. What is the test statistic? a. 1.27 b. 0.01 c. 4.23 d. 100 14. What is the p-value? a. 10.2% b. 0% c. 49.48% d. 0.65% 15. What is your conclusion? a. Reject the null hypothesis b. Accept the null hypothesis c. Do not reject the null hypothesis d. Do not accept the alternate hypothesis

Data collected on the yearly demand for 50-pound bags of fertilizer at Wallace Garden Supply are shown in the following table. Compare the exponential smoothing with a smoothing constant of 0.3 and a three-year moving average forecasting method, which method do you think is better (use mean absolute deviation MAD for your analysis)? how to analyze each in excel and what determines which is best method?

Group of answer choices

The three-year moving average is better.

Can no tell from the data given.

The exponential smoothing method is better

When smoothing constant equal to 0.3, it becomes the same model as the three-year moving average.

A very busy and fancy restaurant records the wait time for each customer that comes in. Below are 12 customers’ wait times (in minutes):

51        60        59        72        80        83        54        66        61        81        66        62

1.The manager wants to know if there is evidence that the true mean wait time is greater than 1 hour. What are the null and alternative hypotheses to test the claim? Will this be a one-sided or two-sided test?

2.Assuming that σ = 20 minutes, what is the test statistic for testing the hypotheses?

3.What is the corresponding p-value?

4.Do you reject the null hypothesis based on a significance level of .05? What conclusion should you tell the manager?

5.In practice, we do not know the population standard deviation. What would be the test statistic for testing the same hypotheses from (1.)?

6.According to the table of t critical values and assuming a significance level of α = .05, what is the critical value for rejecting the null hypothesis? What conclusion would you make?

In a sample of 270 adults, 216 had children. Construct a 99% confidence interval for the true population proportion of adults with children. Give your answers as decimals, to three places

A very busy and fancy restaurant records the wait time for each customer that comes in. Below are 12 customers’ wait times (in minutes):

51        60        59        72        80        83        54        66        61        81        66        62

1. Assuming that the true mean wait time is 70 minutes with a variance of 9 minutes, what is the probability that a customer will wait between 65 to 80 minutes?

2. What is the standard deviation of the sampling distribution of x̄, the average wait time?

3. In practice we do not know the population mean wait time. Assuming this, construct and interpret a 90% confidence interval for μ, the true mean wait time. Assume that σ = 20 minutes.

4.In practice, we do not know the population standard deviation. Assuming this, construct and interpret a 95% confidence interval for μ, the true mean wait time. Assume that σ is unknown.

5.The manager wants to know if there is evidence that the true mean wait time is greater than 1 hour. What are the null and alternative hypotheses to test the claim? Will this be a one-sided or two-sided test?

A very busy and fancy restaurant records the wait time for each customer that comes in. Below are 12 customers’ wait times (in minutes):

51        60        59        72        80        83        54        66        61        81        66        62

(a) What is the mean wait time?

(b) What is the median wait time?

(c) What is the variance in wait times?

(d) What is the unbiased standard deviation in wait times? Why would the standard deviation be more informative of a statistic than the variance?

(e) What is the first quartile? Third quartile?

(g) List the 5 number summary of the data.