You are given data from a company that recently laid off a large number of workers. The data includes the following variables:

Age of the employee

Number of years of education

Marital status (1=married/0=single)

Number of years that the employee worked for the company

Was a manager (1=yes/0=no)

Was in sales (1=yes/0=no)

Was primary earner in the family (1=yes/0=no)

95% confidence interval for proportion of employees who were in sales before they were laid off.

What do the confidence intervals tell you about the typical employee who got laid off?

Are low-fat diets or low-carb diets more effective for weight loss? A simple random sample of 85 adults went on a low-carbohydrate diet for 6 months. At the end of that time, the average weight loss was 4.8 kilograms with a standard deviation 6.04 kilograms. A second simple random sample of 77 adults went on a low-fat diet. Their average weightloss was 4 kilograms with a standard deviation of 5.08 kilograms. Can you conclude that the true mean weightloss differs between the two diets? Use a 10% significance to decide. Group 1: Low-Carb Group 2: Low-Fat Round to the fourth Select the correct alternative sign: μ 1 μ 2 Test Statistic: p-value: Decision Rule: Did Significance Happen? There enough evidence to conclude

A genetic experiment involving peas yielded one sample of offspring consisting of 443 green peas and 120 yellow peas. Use a 0.05 significance level to test the claim that under the same​circumstances, 26​% of offspring peas will be yellow. Identify the null​ hypothesis, alternative​ hypothesis, test​ statistic, P-value, conclusion about the null​ hypothesis, and final conclusion that addresses the original claim. Use the​ P-value method and the normal distribution as an approximation to the binomial distribution. What are the null and alternative​ hypotheses?

1. State the research hypothesis (non-directional) and the null hypothesis. Make sure you include both DV and IV in the hypotheses from #1 above

2.According to the post-hoc results table, which pairs of the cottages do show the statistically significant difference in “Number of traumas experienced” (e.g. “Cottage A vs. B”)?

do you think that Pill and Mark had good reasons fo choosing the research topic initially ?

Let X be a random variable such that P(X = 1) = 0.4 and P(X = 0) = 0.6.  Compute Var(X).

Prove that for a Markov chain on a finite state space, no states are null recurrent.

Your poll of 620 randomly selected residents of a Chicago suburb indicates that 32% of them would support the introduction of a halfway house for drug addicts in their community. Match the following elements needed to construct a 95% confidence interval.

1)Lower limit--------------->A).037

2)Margin of error----------> B)1.96

3)Critical value-----------> C).019

4)Standard error for proportions----------> D).283

1 point) If xx is a binomial random variable, compute P(x)P(x) for each of the following cases:

(a)  P(x≤1),n=5,p=0.3P(x≤1),n=5,p=0.3

P(x)=P(x)=

(b)  P(x>3),n=4,p=0.1P(x>3),n=4,p=0.1

P(x)=P(x)=

(c)  P(x<3),n=7,p=0.7P(x<3),n=7,p=0.7

P(x)=P(x)=

James was eating a bag of candies that came in eight different colors. He noticed that there appeared to be far fewer green candies than any of the other colors and wondered if the true proportion of green candies was lower than the 12.5% that would be expected if all of the candies came in even amounts. For the sake of statistics, he decided that he would need to buy more candy to test his hypothesis. James randomly selected several bags and candies and recorded the color of each piece of candy. He found that out of the first 400 candies that he chose, 39 of them were green.

James conducts a one-proportion hypothesis test at the 5% significance level, to test whether the true proportion of green candies was lower than 12.5%.

(a) H0:p=0.125; Ha:p<0.125, which is a left-tailed test.

(b) Use a TI-83, TI-83 plus, or TI-84 calculator to test whether the true proportion of green candies is less than 12.5%. Identify the test statistic, z, and p-value from the calculator output, rounding to three decimal places.

. Which   of   the   following   is   NOT   CORRECT   about   a   randomized   complete   block   experiment?  

(a)   Every   block   is   randomized   separately   from   every   other   block.  

(b)   Every   treatment   must   appear   at   least   once   in   every   block.  

(c)   Blocking   is   used   to   remove   the   effects   of   another   factor   (not   of   interest)   from   the   comparison   of  

levels   of   the   primary   factor.  

(d)   The   ANOVA   table   will   have   another   line   in   it   for   the   contribution   to   the   variability   from   blocks.  

(e)   Blocks   should   contain   experimental   units   that   are   as   different   as   possible   from   each   other.  

The table below shows performance data for 100 flights between cities A - G for some airline, including: date, flight #, origin, destination, # passengers flown (load), and tardiness (late, in hours).

write a VBA code (N=10000) to simulate the following:

1. (I7): number of flights which were late for at least 0.75 hrs.

2. (I10) average load of flights originated from C with load exceeding 250.

3. (I13): smallest tardiness of flights from B to E between 9/1/18 and 9/3/18.

4. (I16): total load of flights flown from A to C, D, and E on 9/4/18.

5. (I19): the flight # of the flight with the maximal load among all flights from A to G with tardiness less than 0.6 hrs.

The accuracy of a census report on a city in southern California was questioned by some government officials. A random sample of 1215 people living in the city was used to check the report, and the results are shown below.

Using a 1% level of significance, test the claim that the census distribution and the sample distribution agree.

(a) What is the level of significance?

State the null and alternate hypotheses.

H₀: The distributions are different.

H₁: The distributions are different.

H₀: The distributions are the same.

H₁: The distributions are different.    

H₀: The distributions are the same.

H₁: The distributions are the same.

H₀: The distributions are different.

H₁: The distributions are the same.

(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)

Are all the expected frequencies greater than 5?

Yes

No    

What sampling distribution will you use?

uniform

chi-square    

Student's t

normal

binomial

What are the degrees of freedom?

(c) Estimate the P-value of the sample test statistic.

P-value > 0.100

0.050 < P-value < 0.100    

0.025 < P-value < 0.050

0.010 < P-value < 0.025

0.005 < P-value < 0.010

P-value < 0.005

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis that the population fits the specified distribution of categories?

Since the P-value > α, we fail to reject the null hypothesis.

Since the P-value > α, we reject the null hypothesis.    

Since the P-value ≤ α, we reject the null hypothesis.

Since the P-value ≤ α, we fail to reject the null hypothesis.

(e) Interpret your conclusion in the context of the application.

At the 1% level of significance, the evidence is sufficient to conclude that census distribution and the ethnic origin distribution of city residents are different.

At the 1% level of significance, the evidence is insufficient to conclude that census distribution and the ethnic origin distribution of city residents are different.  

Define the three types of hypothesis tests and explain why they are used. Give an example for each.