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;

(1) Consider a normal distribution with mean 38 and standard deviation 3. What is the probability a value selected at random from this distribution is greater than 38? (Round your answer to two decimal places.)

(4) Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.) μ = 14.1; σ = 4.4 P(10 ≤ x ≤ 26)=

(5) Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)

μ = 15.0; σ = 2.8 P(8 ≤ x ≤ 12) =

(6) Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.) μ = 107; σ = 11 P(x ≥ 120) =

(7) Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)

μ = 2.1; σ = 0.39 P(x ≥ 2) =

(8) Find z such that 4.2% of the standard normal curve lies to the left of z. (Round your answer to two decimal places.)
z =

Sketch the area described.

(9)Find z such that 2.7% of the standard normal curve lies to the right of z. (Round your answer to two decimal places).

z=

Sketch the area described

(10) Find the z value such that 86% of the standard normal curve lies between −z and z. (Round your answer to two decimal places.)
z =

Sketch the area described.

(11) Thickness measurements of ancient prehistoric Native American pot shards discovered in a Hopi village are approximately normally distributed, with a mean of 5.3millimeters (mm) and a standard deviation of 0.8 mm. For a randomly found shard, find the following probabilities. (Round your answers to four decimal places.)

(a) the thickness is less than 3.0 mm


(b) the thickness is more than 7.0 mm


(c) the thickness is between 3.0 mm and 7.0 mm

(12) Quick Start Company makes 12-volt car batteries. After many years of product testing, the company knows that the average life of a Quick Start battery is normally distributed, with a mean of 45.2 months and a standard deviation of 8.1 months.

(a) If Quick Start guarantees a full refund on any battery that fails within the 36-month period after purchase, what percentage of its batteries will the company expect to replace? (Round your answer to two decimal places.)
%

(b) If Quick Start does not want to make refunds for more than 11% of its batteries under the full-refund guarantee policy, for how long should the company guarantee the batteries (to the nearest month)?
months

(13) How much should a healthy kitten weigh? Suppose that a healthy 10-week-old (domestic) kitten should weigh an average of μ = 25.3 ounces with a (95% of data) range from 15.0 to 35.6 ounces. Let x be a random variable that represents the weight (in ounces) of a healthy 10-week-old kitten. Assume that x has a distribution that is approximately normal.

(a) The empirical rule (Section 7.1) indicates that for a symmetrical and bell-shaped distribution, approximately 95% of the data lies within two standard deviations of the mean. Therefore, a 95% range of data values extending from μ − 2σ to μ + 2σ is often used for "commonly occurring" data values. Note that the interval from μ − 2σ to μ + 2σ is 4σ in length. This leads to a "rule of thumb" for estimating the standard deviation from a 95% range of data values.Estimating the standard deviation

For a symmetric, bell-shaped distribution,≈

=

where it is estimated that about 95% of the commonly occurring data values fall into this range.Estimate the standard deviation of the x distribution. (Round your answer to two decimal places.)
oz

(b) What is the probability that a healthy 10-week-old kitten will weigh less than 14 ounces? (Round your answer to four decimal places.)


(c) What is the probability that a healthy 10-week-old kitten will weigh more than 33 ounces? (Round your answer to four decimal places.)


(d) What is the probability that a healthy 10-week-old kitten will weigh between 14 and 33 ounces? (Round your answer to four decimal places.)


(e) A kitten whose weight is in the bottom 7% of the probability distribution of weights is called undernourished. What is the cutoff point for the weight of an undernourished kitten? (Round your answer to two decimal places.)
oz

(14) A relay microchip in a telecommunications satellite has a life expectancy that follows a normal distribution with a mean of 93 months and a standard deviation of 3.1 months. When this computer-relay microchip malfunctions, the entire satellite is useless. A large London insurance company is going to insure the satellite for 50 million dollars. Assume that the only part of the satellite in question is the microchip. All other components will work indefinitely.

(a) For how many months should the satellite be insured to be 90% confident that it will last beyond the insurance date? (Round your answer to the nearest month.)
months

(b) If the satellite is insured for 84 months, what is the probability that it will malfunction before the insurance coverage ends? (Round your answer to four decimal places.)


(c) If the satellite is insured for 84 months, what is the expected loss to the insurance company? (Round your answer to the nearest dollar.)
$  

(d) If the insurance company charges $3 million for 84 months of insurance, how much profit does the company expect to make? (Round your answer to the nearest dollar.)

(14) The amount of money spent weekly on cleaning, maintenance, and repairs at a large restaurant was observed over a long period of time to be approximately normally distributed, with mean μ = $627 and standard deviation σ = $46.

(a) If $646 is budgeted for next week, what is the probability that the actual costs will exceed the budgeted amount? (Round your answer to four decimal places.)


(b) How much should be budgeted for weekly repairs, cleaning, and maintenance so that the probability that the budgeted amount will be exceeded in a given week is only 0.14? (Round your answer to the nearest dollar.)

Suppose three competing airlines each schedule their own flight to Waco which arrives there between 2:00 and 3:00 pm according to a continuous uniform distribution. All three flights are mutually independent.

(a) If Ralph shows up at the airport at 2:00 and decides he will watch all three arrivals, what is the expected time that he observes the third and last arrival?

(b) If each airline’s flight only stays on the ground for 10 minutes, find or estimate the probability that all 3 airlines will have a plane on the ground at Waco at some point in the hour from 2:00 to 3:00.

The weight of Coca Cola cans is being analyzed. Thirteen cans, randomly selected from the process, are measured, and the results are as follows (in fluid ounces): 16.01, 16.01, 16.02, 16.03, 16.05, 16.07, 16.02, 16.01, 16.00, 16.01, 16.07, 16.05 and 16.05. Determine the following using the formulas (include all the formulas) and confirm your answer using Minitab. a. Average b. Sample standard deviation c. Median d. Mode e. Range f. Construct histogram using Minitab and determine Kurtosis and skewness (use Minitab only), comment on these values in relation to the histogram.

URGENT

a) samples of rejuvenated mitochondria are mutated (defective) with probability 0.2.find the probability you need to examine at least 6 samples to find 2 samples containing mutations.report answers to 3 decimal places.(try to type your answer)

b) what is the first,second,third quartile, and the outlier of 15,29,30,34,35,36,37,37,37,40,42,42,44,44,45,46,49,51,53,54?(try to type your answer)

c) the claim is that the IQ scores of statistics professors are normally distributed, with a mean less than 126. A sample of 17 professors had a mean IQ score of 125 with a standard deviation of 10. find the value of the test statistic?