A study randomly selected 100 samples, each of which consisted of 100 people, and recorded the number of left-handed people, X. The table below shows the probability distribution of the data. Find the mean and the standard deviation of the probability distribution using Excel.

• Round the mean and standard deviation to two decimal places.

Let U be a Standard Uniform random variable. Show all the steps required to generate:

1. a Binomial random variable with parameters n = 12 and p = 0.6
2. a discrete random variable with the distribution P(x), where P(0) = 0.4, P(3) = 0.1, P(7) = 0.2, P(14) = 0.3;
3. a continuous random variable with the density f(x) = 4x 3 , 0 < x < 1;
4. a continuous random variable with the density f(x) = (1/18)x 2 , -3 < x < 3;
5. a continuous random variable with the density f(x) = (5/128)x 1/4 , 0 < x < 16

1. McDonald’s makes the claim that it takes 90 seconds or less from the time a car stops at the order point to delivery of an order through the window. How can McDonald’s substantiate this claim when drive-thru times vary?
2. How does McDonald’s quantify the uncertainty surrounding its estimate of drive-thru service time?
3. How can the variability in drive-thru service times be quantified? Why is it important to understand variability?
4. Why is it important for McDonald’s to effectively communicate its statistical findings? What types of decisions depend on these data?

As a newly hired manager of a company that provides cell phone service, you want to determine the percentage of adults in your state who live in a household with cell phones and no land-line phones. How many adults must you survey? Assume that you want to be 90% confident that the sample percentage is within 4 percentage points of the true population percentage.

In a test of effectiveness of garlic for lowering cholesterol, 47 subjects were treated with Garlicin, which is garlic in a processed tablet form. Cholesterol levels were measured before and after the treatment. The changes in their levels of LDL cholesterol (in mg/dL) have a mean of 3.2 and a standard deviation of 18.6.

Organic chemists often purify organic compounds by a method known as fractional crystallization. An experimenter wanted to prepare and purify 4.85 g of aniline. Ten 4.85 g quantities of aniline were individually prepared and purified to acetanilide. The following dry yields were recorded.

Estimate the mean grams of acetanilide that can be recovered from an initial amount of 4.85 g of aniline. Use a 95% confidence interval. (Round your answers to three decimal places.)
g to  g

Five students take statistics one semester and college algebra the next semester. Their overall course grades (%) are listed in the table.

a. Which statistical procedure, listed in the Assessment, would be most appropriate to test the claim "student overall course grades are the same in both courses"? Options are:
t-Test: Paired Two Sample for Means

t-Test: Two-Sample Assuming Equal Variances

t-Test: Two-Sample Assuming Unequal Variances

z-Test: Two Sample for Means

b. Is there sufficient evidence at the 95% significance level to reject the null hypothesis? Explain

Use Excel to develop a regression model for the Hospital Database to predict the number of Personnel by the number of Births. How many residuals are within 1 standard error? Write your answer as a whole number.

An elevator has a placard stating that the maximum capacity is 1560 lb—10 passengers.​ So, 10 adult male passengers can have a mean weight of up to 1560/10=156 pounds. If the elevator is loaded with

10 adult male​ passengers, find the probability that it is overloaded because they have a mean weight greater than 156 lb.​ (Assume that weights of males are normally distributed with a mean of 165 lb and a standard deviation of 28 lb​.) Does this elevator appear to be​ safe?

The probability the elevator is overloaded is ___​(Round to four decimal places as​ needed.)

Does this elevator appear to be​ safe?

A. Yes, 10 randomly selected people will always be under the weight limit.

B. ​No, there is a good chance that 10 randomly selected people will exceed the elevator capacity.

C. ​No, 10 randomly selected people will never be under the weight limit.

D. ​Yes, there is a good chance that 10 randomly selected people will not exceed the elevator capacity.

1.) Different types of bees are very similar in appearance. Statistical analysis of certain measurements, like wing width, can be used to distinguish one kind of bee from another. A random sample of 10 bees is taken from a hive and the wing widths are given below.

Wing Width Measurements (mm)

95% of all samples of 10 bees of the type taken from hive will be within how many millimeters (mm)of the sample mean given by the wing width measurements in table above. Hint: You are calculating the margin of error associated with 95% confidence interval. Round answer to 4 decimal places.

2.)

A police department observed 50 out of 89 motorists that went through an intersection were speeding.

A 99% confidence interval for the proportion of those speeding through the intersection is (0.42633,0.69727)

City council has agreed to put a stop sign at the intersection if it can be proved that more than 50% of all motorists speed through it.

Based on this information what conclusions can be drawn from confidence interval? Select all that apply.

Select one or more:

a. A 95% confidence interval for the same sample would be narrower than the 99% confidence interval

b. A 95% confidence interval for the same sample would be wider than the 99% confidence interval

c. If this study were repeated, there is a 99% probability that the calculated confidence interval would contain the true proportion of everyone speeding through intersection.

d. There is enough evidence to conclude more than 50% of all motorists are speeding through intersection

e. There is not enough evidence to conclude more than 50% of all motorists are speeding through intersection

1.) A recent survey showed that high school girls average 110 text messages daily. The population standard deviation is 25 text messages. 1 In repeated samples of size n = 64 high school girls, the expected value of the sample mean is,

a 1.719 b 10.488 c 13.75 d 110

2.) In repeated samples of size n = 64 high school girls, the standard error of the sample mean is,

a 25 b 5 c 3.125 d 0.391

3.) In repeated samples of size n = 64 high school girls, the fraction of sample means that fall within ±5 messages from the population mean is,

a 0.8904 b 0.9260 c 0.9538 d 0.9824

4.) The margin of error for the middle interval which includes 95% of means from samples of size n = 64 is,

a 5.763 b 5.941 c 6.125 d 6.248

Use Excel to develop a regression model for the Hospital Database to predict the number of Personnel by the number of Births. How many residuals are within 1 standard error? Write your answer as a whole number.

The following are body mass index (BMI) scores measured in 12 patients who are free of diabetes and are participating in a study of risk factors for obesity. Body mass index is measured as the ratio of weight in kilograms to height in meters squared. Generate a 95% confidence interval estimate of the true BMI.

25 27      31      33      26   28      38   41   24   32   35      40

1) In a study, the final statistical analysis showed that r square=0.35 (p<0.01). Which one of the following interpretations best explains this results?

A) The model explains 65% of the variation in the outcome, because 1.00-0.35=65%.

B) No conclusions can be drawn because it is not apparent whether the estimated coefficients for each covariate were statistically significant.

C) About 35% of the variation in the outcome was explained by the independent variable(s).

D) The model explains about 35% of the variation for independent variable(s).

2) Which of followings refers the multicollinearity problem?

A) Some independent variables are strongly correlated each other.

B) When the coefficient for a product of two independent variables (X₁*X₂) is statistical significant (p<0.05).

C) There is an interaction effect between two independent variables.

D) It will occur when linear regression encounters step-wise regression.

3) A PGY1 post-graduate conducted a survey study in her community. Of 10,000 surveyed residents, there are 200 persons with diabetes mellitus, 50 persons with heart disease and 20 persons with both diabetes and heart disease.   If a selected resident has diabetes mellitus, what is the probability that this same individual also has heart disease? (Clue: need to calculate the relevant probability).

A) 10%

B) 20%

C) 0.2%

D) 40%

E) 0.5%

4) A clinical research plans to conduct a linear regression analysis to assess the Health related quality of life score which is the primary outcome with continuous data. The health outcomes will be regressed on 10 predictors or confounding factors including age, sex, race, BMI, health education, family incomes, number of years disease on set, etc. Based on our discussion in the lecture, how many patients at least does he/she need to recruit for this linear regression?

A) 50

B) 150

C) 200

D) 1500

E) 30

5) Since you learned the multiple linear regression analysis in class, you are given the following linear regression model:   Y (female life expectancy) = 82.7 – 0.12 * (fertility number) – 0.24 * (infant mortality per 1000). Please predict the female life expectancy in Ghana country where fertility number = 5.8 and infant mortality per 1000 = 58.3.

A) 80.7

B) 68.0

C) 57.6

D) 69.0

6) A research scientist conducted a factorial ANOVA for her clinical study, which involved 5 different therapy regimens in each of four different hospital settings. In order to assess the therapy effect, the pharmacist would like to evaluate any interaction effect between hospital and regimen. The degree of freedom for interaction is equal to:

A) 7

B) 12

C) 8

D) 20

E) 6

7) There are two kinds of influential statistics: parametric vs. non-parametric statistics. Which of followings is NOT parametric influential statistics?

A) Student t-test

B) F-test

C) Two-way ANOVA

D) Wilcoxon test

E) ANCOVA

Suppose that the service life, in yours, of the "LOUD WHISPER", a hearing aid battery, is a random variable having a Weibull distribution with the Scale parameter = 0.7 and the Shape parameter = 2.1.

a) What is the hazard rate at the second year of operation?

b) What is the probability that the battery will fail between the first and third year?

c) At what point in time, 30% of the batteries have died?