Tests in one teacher’s past classes have scores with a standard deviation equal to 14.1. One of their recent classes has 27 test scores with a standard deviation of 9.3. Use a 0.01 significance level to test the claim that this recent class has less variation than past classes. (15 points) a. Hypothesis (steps 1-3): b. Value of Test Statistic (steps 5-6): c. P-value (step 6): d. Decision (steps 4 and 7): e. Conclusion (step 8):

Miles  Freq
 0-4     3
 5-9    14
10-14   13
15-19    4

Write two sentences for non-statisticians expressing Chebyshev’s Theorem. Select the most appropriate sentence corresponding to two standard deviations.

*About 68% of students drive between 5.5212 miles and 13.7730 miles to somewhere
*At least 88.9% of students drive between -2.7306 miles and 22.0248 miles to 
*About 99.7% of students drive between 1.3953 miles and 17.8989 miles to 
*About 68% of students drive less than 22.0248 miles to
*About 95% of students drive between 5.5212 miles and 13.7730 miles to
*About 99.7% of students drive between -2.7306 miles and 22.0248 miles to
*About 68% of students drive between 1.3953 miles and 17.8989 miles to
*About 99.7% of students drive between 5.5212 miles and 13.7730 miles to
*At least 75% of students drive between -2.7306 miles and 22.0248 miles to
*At least 75% of students drive less than 22.0248 miles to
*About 95% of students drive between 1.3953 miles and 17.8989 miles to
*At least 75% of students drive between 1.3953 miles and 17.8989 miles to
*About 95% of students drive less than 22.0248 miles to 
*At least 88.9% of students drive between 1.3953 miles and 17.8989 miles to
*About 99.7% of students drive less than 22.0248 miles to
*About 95% of students drive between -2.7306 miles and 22.0248 miles to
*At least 88.9% of students drive less than 22.0248 miles to
*About 68% of students drive between -2.7306 miles and 22.0248 miles to

Select all of the possible alternative hypotheses from the list below.

Question options

p = 0.37

p>0.84

p<0.42

p≠0.10

a) A 13-card Bridge hand is dealt from a standard deck. What is the percentage chance that the hand contains exactly 6 spades or exactly 6 hearts or exactly 6 diamonds? Be sure to give your answer as a percentage, not as a probability.

B) A 13-card Bridge hand is dealt from a standard deck. What is the percentage chance that the hand contains exactly 2 Aces or exactly 2 Kings? Be sure to give your answer as a percentage, not as a probability.

Suppose you are conducting a quantitative research study for a major car dealership in the United States with the objective to rate the importance of typical obstacles in consumers' car purchasing process (such as long wait times, complicated paperwork, aggressive salespeople, or insufficiently trained sales executives). Suppose you came to the conclusion that a random sample is not feasible or cost effective for this study. Which of the following nonprobability sampling designs (convenience sampling, judgment sampling, quota sampling, or snowball sampling) would you prefer for your study? And which of these four sampling design would be the least desirable? Please justify your assessment.

How to set up experimental design for 3 factors at 4 different levels. I get in total I should end up with 81 experimental runs. Can you help me to determine how to distribute these 4 levels across 3 factors?

Consider flipping nn times a coin. The probability for heads is given by pp where pp is some parameter which can be chosen from the interval (0,1)(0,1).

Write a Python code to simulate nn coin flips with heads probability pp and compute the running proportion of heads X¯nX¯n for nn running from 1 to 1,000 trials. Plot your results. Your plot should illustrate how the proportion of heads appears to converge to pp as nn approaches 1,000.

In [ ]:

### Insert your code here for simulating the coin flips and for computing the average

​

​

In [2]:

### Complete the plot commands accordingly for also plotting the computed running averages in the graph below

​

p = 0.25 # just an example

​

plt.figure(figsize=(10,5))

plt.title("Proportion of heads in 1,000 coin flips")

plt.plot(np.arange(1000),p*np.ones(1000),'-',color="red",label="true probability") 

plt.xlabel("Number of coin flips")

plt.ylabel("Running average")

plt.legend(loc="upper right")

For an irreducible Markov chain, either all states are positive recurrent or none are. Prove.

Consider the following results for independent samples taken from two populations.

(a) What is the point estimate of the difference between the two population proportions?

(b) Develop a 90% confidence interval for the difference between the two population proportions.

(c) Develop a 95% confidence interval for the difference between the two population proportions.

The following table shows the Myers-Briggs personality preferences for a random sample of 400 people in the listed professions.

Use the chi-square test to determine if the listed occupations and personality preferences are independent at the 0.01 level of significance.Find (or estimate) the P-value of the sample test statistic.

Suppose a survey was done this year to find out what percentage of all Americans own a bread machine. Out of their random sample of 1,000 Americans, 300 own a bread machine. The margin of error of 95% confidence interval for this survey was plus or minus 3%.

95% confidence interval will be

CNNBC recently reported that the mean annual cost of auto insurance is 960 dollars. Assume the standard deviation is 213 dollars. You take a simple random sample of 70 auto insurance policies. Find the probability that a single randomly selected value is less than 995 dollars. P(X < 995) = Find the probability that a sample of size n = 70 is randomly selected with a mean less than 995 dollars. P(M < 995) =

We wish to determine if a two sections of the same introductory course have significantly different “success rates” (defined as the proportion of students who receive a course grade of A, B, or C). The first section meets in the early morning, the second section meets in the late afternoon. Each section has 70 students. Among the early morning section, 59 receive an A, B, or C. Among the late afternoon section, 49 receive an A, B, or C.. Assume these can be treated as independent simple random samples from their respective populations. Use this sample data to test the claim H0:(p1−p2)=0 against HA:(p1−p2)≠0, using a significance level of 5%.

The value of the test statistic is z=

(round to at least four decimal places).

The P-value for this sample is

A social media platform wants to determine if there is a significant difference between the average weekly usage (number of minutes spent on the site per week) of female users and male users, and plans to conduct a Hypothesis Test at the 5% significance level. Let μ1 be the average daily usage among all male users, and μ2 be the average daily usage among all female users.

An appropriate alternative hypothesis is:

In a simple random sample of 35 male users, the mean daily usage is 115.9 mintues, with a standard deviation of 8.07 minutes. An independent simple random sample of 46 female users has a mean daily usage of 113 minutes and a standard deviation of 7.24 minutes.

The value of the test statistic is t=

. The P-Value is

Use the following dataset and assume all assumptions are met

Provide all R code needed to conduct the tests

Bat house color and species

Lasiurus in brown: 45, 49, 53, 54, 46, 51, 50, 48, 52, 50

Myotis in brown: 40, 38, 35, 39, 39, 44, 42, 48, 41, 40

Lasiurus in tan: 53, 49, 51, 52, 59, 54, 53, 54, 58, 51

Myotis in tan: 62, 64, 59, 61, 65, 61, 58, 63, 56, 61

1. Provide the three hypotheses statements (null and alternative) that could be made if a two-factor ANOVA were conducted on this data set.

2. Conduct a two-factor ANOVA and give an explanation for what each of the F statistics reported in the model summary are testing.

3. Interpret the results as reported by the model summary. Provide an explanation addressing each of the hypotheses that were used in this statistical test. Should each of these hypotheses be considered in this analysis?

4. Create a figure that assesses the possibility of a significant second-order interaction and interpret the figure in one sentence.