3. The weights in pounds of 30 preschool children are listed below. Find the five number summary of the data set.

25 25 26 26.5 27 27 27.5 28 28 28.5

29 29 30 30 30.5 31 31 32 32.5 32.5

33 33 34 34.5 35 35 37 37 38 38

4. A manufacturer receives an order for light bulbs. The order requires that the bulbs have a mean life span of 850hours. The manufacturer selects a random sample of 25 light bulbs and finds they have a mean life span of 845 hours with a standard deviation of 15 hours. Assume the data are normally distributed. Using a 95% confidence level, test to determine if the manufacturer is making acceptable light bulbs and include an explanation of your decision.

5. A manufacturer of golf equipment wishes to estimate the number of left-handed golfers. How large of a sample is needed in order to be 95% confident that the sample proportion will not differ from the true proportion by more than 4%.

6.

A local group claims that the police issue at least 60 speeding tickets a day in their area. To prove their point, they randomly select one month. Their research yields the number of tickets issued for each day. The data are listed below. Assume the population standard deviation is 12.2 tickets. At ? = 0.01, test the group’s claim. Make sure to state your conclusion regarding the claim with your reasoning.

70 48 41 68 69 55 70 57 60 83 32 60 72 58 88 48

59 60 56 65 66 60 68 42 57 59 49 70 75 63 44

7. A local politician, running for reelection, claims that the mean prison time for car thieves is less than the required 4 years. A sample of 80 convicted car thieves was randomly selected, and the mean length of prison time was found to be 3.5 years. Assume the population standard deviation is 1.25 years. At ? = 0.05, test the politician’s claim. Make sure to state your conclusion regarding the claim with your reasoning.

According to a Virginia Tech survey, college students make an average of 11 cell phone calls per day. Moreover, 80% of the students surveyed indicated that their parents pay their cell phone expenses (J. Elliot, “Professor Researches Cell Phone Usage Among Students,” www.physorg.com, February 26, 2007).

1. If you select a student at random, what is the probability that he or she makes more than 10 calls in a day? More than 15? More than 20?

2. If you select a random sample of 10 students, what distribution can you use to model the proportion of students who have parents who pay their cell phone expenses?

3. Using the distribution selected in (c), what is the probability that all 10 have parents who pay their cell phone expenses? At least 9? At least 8?

d. Identify the pair of independent variables that are the most strongly related to each other.

e. Identify the pair of independent variables that are the least strongly related to each other.

f. For the answer to part d, test to see if the population correlation coefficient (rho) for those two variables is different from zero. Use alpha = 0.05.

g. For the answer to part e, test to see if the population correlation coefficient (rho) for those two variables is different from zero. Use alpha = 0.05.

Excel sheet in link

https://docs.google.com/spreadsheets/d/1TL7blpx16llIqr_iLw_4D-V0n__f9dnvS57OZumxhXQ/edit?usp=sharing

In excell

• t-Test Assuming Equal Variances
• t-Test With Paired Two Samples for Means
• Analysis of Variance
• Correlation Coefficient
• Simple Regression

Skills and self-esteem are believed to influence job performance. To investigate this, an experimenter split 14 recent parolees into "high skill and self-esteem" and "low skill and self-esteem" groups. Three months later, employers were asked to rate each parolee’s job performance on a standard test that gives ratings from 1 to 10, with 10 being the highest. The following ratings were obtained for the individuals in the two groups:

a. Run descriptive statistics on the data. Please provide measures of central tendency and variability for the entire sample and also by groups.

b. Are there differences in job performance between the two groups? In your response, provide the answers to the following:

(i) The test you will run.

(ii) The null and research hypothesis.

(iii) The test results (copy the results to the word doc).

(iv) Your interpretation of the results.

Please do this task by R.

a) Revise the simulation shown in the lecture with the aim of constructing the empirical sampling distribution of beta_hat, based on 5000 trials.

b) According to the lecture, the mean of that histogram is supposed to be approximately equal to the true slope. Is it? Show code.

c) According to the lecture, the standard deviation of that histogram is supposed to be approximately equal to sigma_eps/sqrt(Sxx). Is it? Show code.

d) According to the lecture, the distribution of the beta_hat is supposed to be normal with certain parameters. Use qqnorm() and abline() to confirm that it is normal.

not sure if this help or not,

n = 10

n.trial = 64

x = c(1:n)

y_true = 10 + 2*x

sigma_eps = 15

par(mfrow=c(8,8),mar=c(0,0,0,0))

set.seed(123)

for(trial in 1:n.trial){

y_obs = y_true + rnorm(n,0,sigma_eps)

lm.1 = lm(y_obs ~ x)

plot(x, y_obs)

abline(10,2, col=2)

abline(lm.1, col=4)

}

Out of the variables provided below:

1) Select one dependent variable, one primary independent variable, and one potential confounding variable that will be used for linear regression.

2) State a possible research question and hypotheses (null and alternative) for these variables

Variables: Sex, Age, Education Level, Smoking Status, Employed, Minutes Exercised, Annual Income, Neighborhood

Using traditional methods, it takes 104 hours to receive a basic driving license. A new license training method using Computer Aided Instruction (CAI) has been proposed. A researcher used the technique with 100 students and observed that they had a mean of 105 hours. Assume the standard deviation is known to be 5. A level of significance of 0.05 will be used to determine if the technique performs differently than the traditional method. Is there sufficient evidence to support the claim that the technique performs differently than the traditional method?

The median US salary is $50,700, according to US Census data. Using a one-sample

t-test, test to see if participant income (INC1) is different from the national average. Use a two-tailed test and an alpha level of 5%.

1. Participant income is significantly greater than the national average
2. Participant income is significantly less than the national average
3. Participant income is not significantly different from the national average
4. Participant income cannot be compared to the national average

One-Sample Statistics

INCOME N=400 Mean=$47,112.92 Std. Deviation=$40,477.089 Std. Error Mean=$2,023.854

One-Sample Test

Test Value = 0

INCOME t=23.279 df=399 Sig. (2-tailed)=.000 Mean Difference=$47,112.920

95% Confidence Interval of the Difference

(lower)$43,134.17 (higher)$51,091.67

Beer drinkers order an average of 50 pitchers of beer per hour at Nick's Pub in

Bloomington, Indiana. Answer the following questions:

• What is the probability that at least 100 pitchers are ordered in a three-hour period?

• What is the chance that the time between ordered pitchers will be 45 seconds or less?

B.An average of 100 customers arrive each hour at the Central Forest Coffee Shop. What

is the probability that at least 170 customers arrive in a two-hour period?

An environmentalist wants to find out the fraction of oil tankers that have spills each month.

Step 2 of 2 :  

Suppose a sample of 516 tankers is drawn. Of these ships, 393 did not have spills. Using the data, construct the 90% confidence interval for the population proportion of oil tankers that have spills each month. Round your answers to three decimal places.

According to a recent article, 32% of drivers had driven drowsy in the past month. (Source: Thenationshealth.aphapublications.org/content/41/10/E52.fuII)

Suppose law enforcement officials are planning a survey of 1000 drivers to determine what proportion are driving drowsy.

a. Is whether a driver has driven drowsy in the past month qualitative or quantitative?

b. Would it be unusual if, in a random sample of 1000 drivers, 35% or more were driving drowsy in the last month? Include justifications for full credit.

c. What is the minimum number of drivers that must be sampled to be sure that the shape is approximately normal? Hint – use the formula

what applied statistical strengths exist in analyzing of TV and/or movie ratings?aa

A distribution of values is normal with a mean of 80 and a standard deviation of 18. From this distribution, you are drawing samples of size 13. Find the interval containing the middle-most 32% of sample means: Incorrect Enter your answer using interval notation. In this context, either inclusive or exclusive intervals would be acceptable. Your numbers should be accurate to 1 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

What’s the difference between parametric and non-parametric measures.