Question text

7-step Hypothesis Testing Problem

Complete the 7 steps in Excel and upload the file here

Two major automobile manufacturers have produced compact cars with the same size engines.We are interested in determining whether or not there is a significant difference in the MPG (miles per gallon) of the two brands of automobiles.A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance.The following data show the results of the test.

At the 0.05 level of significance, conduct a 7-step hypothesis test to determine whether there is a significant difference in the MPG (miles per gallon) of the two brands of automobiles.

The director of the IRS has been flooded with complaints that people must wait more than 45 minutes before seeing an IRS representative. To determine the validity of these complaints, the IRS randomly selects 400 people entering IRS offices across the country and records the times that they must wait before  seeing an IRS representative. The average waiting time for the sample is 55 minutes with a standard deviation of 15 minutes.

a. What is the population being studied?

b. Are the complaints substantiated by the data at alpha level of 0.10?

**** Please include these Steps****

Step 1 : Define the hypothesis to be texted for Null hypothesis and Alternative hypothesis.

Step 2: Select the appropriate statistical measure, such as the population mean, proportion, or variance

Step 3: Determine whether the alternative hypothesis should be one-sided or two-sided.

Step 4: State the hypotheses using the statistical measure found in Step 2

Step 5: Specify α, the level of the test. α =_______

Step 6: Select the appropriate test statistic based on the information at hand and the assumptions you willing to make. Normal distribution

Step 7 : Determine the critical value of the test statistic

Step 8: Collect sample data and compute the value of the test statistic.

Step 9: Make the decision

Step 10 : State the conclusion in terms of the original question

A box contains eight chips numbered 1 through 8. You randomly select three at random without

replacement.

(a) What is the probability that the largest chip selected is chip number 5?

(b) What is the probability that you select two odd numbered chips and a even numbered chip?

(c) What is the probability that at least one of the chips is numbered 6 or higher?

Please include any theorems or principles you use in your explanation. Thank you.

12.26  Does haptic feedback improve performance?

A group of technology students is interested in whether haptic feedback (forces and vibrations applied through a joystick) is helpful in navigating a simulated game environment they created. To investigate this, they randomly assign 20 students to each of three joystick controller types and record the time (seconds) it takes to complete a navigation mission. The joystick types are (1) a standard video game joystick, (2) a game joystick with force feedback, and (3) a game joystick with vibration feedback. Using the table below of group means and standard deviations, construct an ANOVA table. Based on the F statistic and degrees of freedom, compute the P-value. What do you conclude?

3. Discuss why a researcher needs to be concerned about the survey response rate. What are the implications of a survey having a low response rate?

2. Battery Level of Laptop Computers in Shipment A computer manufacturer ships laptop computers with the batteries fully charged so that customers can begin to use their purchases right out of the box. In its last model, 85% of customers received fully charged batteries. To simulate arrivals, the company shipped 100 new model laptops (randomly picked from their warehouse) to various company sites around the country. Of 100 laptops shipped, 96 of them arrived reading 100% charged. Do the data provide evidence that the proportion of new model laptop computers arrived fully charged to various company sites around the country of a computer manufacturer is higher than the last model? Test an appropriate hypothesis at α = 0.05? Use RStudio.

1. Label the parameter: (4 points)

2. State null and alternative hypotheses: (6 points)

H₀:

H_a:

3. Propose an appropriate hypothesis test: (4 points)

4. Verify the required conditions for the proposed hypothesis test: (8 points)

Randomization assumption:

Normality assumption:

5. Find test statistic and p-value: (9 points)

Test statistic = 

p-value = 

Note: For your future reference, save your R codes and outputs on your machine:

6. Interpret test statistic: (4 points)

7. Interpret the P-value in context: (6 points)

8. Make a decision of hypothesis test: (4 points)

1. Make a conclusion of hypothesis test in context: (5 points)

2. Think of an example of a research question that would be appropriate for using quantitative or qualitative data. How are they similar and how are they different?

4. Identify situations where open-ended questions are more appropriate than closed-ended questions. Think about the advantage of using closed-ended questions over open-ended questions?

3. What are the advantages and disadvantages in using proportional stratified sampling and disproportional stratified sampling?

USING EXCEL

1.         For the most part, our multiple-choice quiz (and Evaluation) questions have four possible answers. (Yes, I know. I throw in an extra answer now and then!)   Suppose you come to a quiz hoping to guess your way through to a decent grade. Find the probability of guessing at least 5 out of the 10 multiple-choice questions correctly, using BINOM.DIST with pdf (i.e., summing each of the individual probabilities of 5, 6, ….., 9, 10), and then with cdf (i.e., taking the complement of one of the cdf values.) Round (final answer only) to 3 digits. Do not round your intermediate answers.

Make sure you label your two methods, “Method 1” and “Method 2” so that they serve as headers for the work you display beneath each.

So would you consider this event likely or unlikely to occur? Explain your answer.

Review: using BINOM.DIST(x, n, p, false) is the pdf function, since the false tells you that this is the probability for only x successes out of n trials with a probability, p, on any trial.

For example, if you’re interested in computing P(X=10) for n = 20, p = .5, then enter

“BINOM.DIST(10,20,5, FALSE)”

However, if you wish to calculate the P(X ≤ 10), enter

“BINOM.DIST(10,20,.5,TRUE)”, since “TRUE” indicates that you wish Excel to give the cumulative probability, that is the sum of the following probabilities:

P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)+…+P(X=10); whereas inserting

“FALSE” gives you only P(X=10).

2.         Now answer the same questions in (a), assuming that each of our weekly quiz questions has 5 answers instead of 4. Again, use both methods, making sure to label your work “Method 1” and “Method 2”.

1. Given the data set A = {5, 4, 6, 14, 2, 2, 11, 4, 5, 8, 3, 1, 12, 15, 13}, which is the data of a sample taken from a larger population.
   1. Calculate the arithmetic mean
   2. Find the median
   3. Find the mode
   4. Calculate the range
   5. Calculate the interquartile range
   6. Calculate the mean deviation
   7. Calculate the variance
   8. Calculate the standard deviation

1. Can we conclude that employee age helps in predicting average employee salary? Follow the 7 steps for hypothesis testing. (10 points)
2. Find the sample regression equation and interpret the coefficients. Remember your interpretations should be in terms of the problem. (4 points)
3. Find the coefficient of determination, and interpret its value. (3 points)
4. Use residual analysis to check the validity of the model and fully explain your findings and conclusions. (6 points)
5. Estimate with 95% confidence the average employee salary for all employees that are 35 years old. Predict with 95% confidence the estimated salary for an individual employee that is 35 years old. Write at least one sentence using your confidence interval and at least one sentence using your prediction interval. (6 points)
6. Verify that the p-value for the F is the same as the slope’s t statistic’s p-value, and show that t² = F. (3 points)
7. Attach or include the relevant Minitab output. (6 points)

A Gallup Poll showed that 44% of Americans are satisfied with the way things are going in the United States. Suppose a sample of 25 Americans are selected. Based on this information, generate a cumulative binomial probability.

Find the probability that no less than 10 Americans are satisfied with the way things are going.

Find the probability that exactly 15 Americans are not satified with the way things are going.

Find the probability that the number of Americans who are satified with the way things are going differs by greater than 2 from the mean.

Find the probability that greater than 4 Americans are satified with the way things are going.

Find the probability that at least 17 Americans are not satified with the way things are going.

Find the probability that no more than 5 Americans are satified with the way things are going.

Find the probability that more than 25% but at most 50% of these Americans are satified with the way things are going.

In a test of the quality of two television commercials, each commercial was shown in a separate test area six times over a one-week period. The following week a telephone survey was conducted to identify individuals who had seen the commercials. Those individuals were asked to state the primary message in the commercials. The following results were recorded.

Commercial A Commercial B

Number who saw the commercial: 155 Number who saw the commercial: 204

Number who recalled the message: 64 Number who recalled the message: 63

Use a=.05 and test the hypothesis that there is no difference in the recall proportions for the two commercials.

Formulate the null and the alternative hypotheses.

What is the value of the test statistic?

What is the p-value( round to 4 decimals)

Compute a 95% confidence interval for the difference between the recall proportions for the two populations (to 4 decimals).

( , )

I am creating SAS code, but am receiving an errors "

ERROR: Value is out of range or inappropriate.

ERROR: No body file. HTML5(WEB) output will not be created."

This is the code:

option ls=65 ps=65;

data one;

input IQ;

cards;

145

139

122

;

title 'Normal Quantile - Quantile Plot for IQ';

ods graphics on;

proc univariate data=one;

qqplot IQ / normal (mu=est sigma=est);

run;