Below are 50 random numbers taken from a random number generator.

a) Using 5 class intervals, determine the computed chi-square value. Answer in 1 decimal place.   

b) What is the critical value of chi-square at 0.05 level of significance. Answer in 2 decimal places.

c) Are the random numbers uniform? Answer YES or NO.

Q7. Here are summary statistics for randomly selected weights of newborn​ girls: n=210​, x overbarx=28.9 ​hg, s=6.3hg. Construct a confidence interval estimate of the mean. Use a 99​% confidence level. Are these results very different from the confidence interval 27.0 hgless than

What is the confidence interval for the population mean muμ​?

____hgless than

The Transportation Security Administration (TSA) collects data on wait time at each of its airport security checkpoints. For flights departing from Terminal 3 at John F. Kennedy International Airport (JFK) between 3:00 and 4:00 PM on Wednesday, the mean wait time is 12 minutes, and the maximum wait time is 16 minutes. [Source: Transportation Security Administration, summary statistics based on historical data collected between February 18, 2008, and March 17, 2008.]

Assume that x, the wait time at the Terminal 3 checkpoint at JFK for flights departing between 3:00 and 4:00 PM on Wednesday, is uniformly distributed between 8 and 16 minutes.

Use the Distributions tool to help you answer the questions that follow.

0123NormalStandard NormalUniform

Select a Distribution

The height of the graph of the probability density function f(x) varies with X as follows (round to four decimal places):

You are flying out of Terminal 3 at JFK on a Wednesday afternoon between 3:00 and 4:00 PM. You get stuck in a traffic jam on the way to the airport, and if it takes you longer than 12 minutes to clear security, you’ll miss your flight. The probability that you'll miss your flight is-------------------- .

You have arrived at the airport and have been waiting 10 minutes at the security checkpoint. Recall that if you spend more than 12 minutes clearing security, you will miss your flight. Now what is the probability that you'll miss your flight?

a. 0.25

b. 0.6667

c. 0.5

d. 0.8333

An automobile battery manufacturer offers a 39/50 warranty on its batteries. The first number in the warranty code is the free-replacement period; the second number is the prorated-credit period. Under this warranty, if a battery fails within 39 months of purchase, the manufacturer replaces the battery at no charge to the consumer. If the battery fails after 39 months but within 50 months, the manufacturer provides a prorated credit toward the purchase of a new battery.

The manufacturer assumes that X, the lifetime of its auto batteries, is normally distributed with a mean of 44 months and a standard deviation of 3.6 months.

Use the following Distributions tool to help you answer the questions that follow. (Hint: When you adjust the parameters of a distribution, you must reposition the vertical line (or lines) for the correct areas to be displayed.)

0123BinomialChi-SquareExponentialF DistributionHypergeometricNormalUniform

Select a Distribution

If the manufacturer’s assumptions are correct, it would need to replace------------------------of its batteries free of charge.

The company finds that it is replacing 9.34% of its batteries free of charge. It suspects that its assumption about the standard deviation of the life of its batteries is incorrect. A standard deviation of---------------results in a 9.34% replacement rate.

Using the revised standard deviation for battery life, what percentage of the manufacturer’s batteries don’t qualify for free replacement but do qualify for the prorated credit?

a. 84.95%

b.44.29%

c. 40.66%

d. 5.71%

A consumer buying cooperative tested the effective heating area of 20 different electric space heaters with different wattages. Here are the results.

Click here for the Excel Data File

1. Compute the correlation between the wattage and heating area. Is there a direct or an indirect relationship? (Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.)

2. Conduct a test of hypothesis to determine if it is reasonable that the coefficient is greater than zero. Use the 0.10 significance level. (Negative value should be indicated by a minus sign. Round intermediate calculations and final answer to 3 decimal places.)

H₀: ρ ≤ 0; H₁: ρ > 0 Reject H₀ if t > 1.3304

3. Develop the regression equation for effective heating based on wattage. (Negative value should be indicated by a minus sign. Round your answers to 3 decimal places.)

4. Which heater looks like the “best buy” based on the size of the residual? (Negative value should be indicated by a minus sign. Round residual value to 2 decimal places.)

Bardi Trucking Co., located in Cleveland, Ohio, makes deliveries in the Great Lakes region, the Southeast, and the Northeast. Jim Bardi, the president, is studying the relationship between the distance a shipment must travel and the length of time, in days, it takes the shipment to arrive at its destination. To investigate, Mr. Bardi selected a random sample of 20 shipments made last month. Shipping distance is the independent variable and shipping time is the dependent variable. The results are as follows:

Click here for the Excel Data File

1. Draw a scatter diagram. Based on these data, does it appear that there is a relationship between how many miles a shipment has to go and the time it takes to arrive at its destination?

1. On the graph below, use the point tool to plot the point corresponding to the first Distance and its Shipping Time (Distance 1).

2. Repeat the process for the remainder of the sample (Distance 2, Distance 3, … ).

3. To enter exact coordinates, double-click on the point and enter the exact coordinates of x and y.

1. b-1. Fill in the blanks. (Round your answers to 3 decimal places. Negative values should be indicated by minus sign.)

1. b-2. State the decision rule for 0.05 significance level: H₀: ρ ≤ 0; H₁: ρ > 0. (Round your answer to 3 decimal places.)

1. b-3. Compute the value of the test statistic. (Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.)

1. b-4. Can we conclude that there is a positive correlation between distance and time? Use the 0.05 significance level.

1. c-1. Determine the coefficient of determination. (Round your answer to 3 decimal places.)

1. c-2. Fill in the blank below. (Round your answer to 1 decimal place.)

4. Determine the standard error of estimate. (Round your answer to 3 decimal places.)

5. Would you recommend using the regression equation to predict shipping time?

A factory finds that, on average, 10% of the bulbs produced by a given machine will be defective for certain specified requirements. If 8 bulbs are selected at random from the day's production of this machine, find the probability a.) exactly 2 will be defective. b.) that 2 or more will be defective and c.) that more than 5 will be defective.

A Gallup poll asked a sample of Canadian adults if they thought the law should allow doctors to end the life of a patient who is in great pain and near death if the patient makes a request in writing. The poll included 295 people in Quebec, 230 of whom agreed that doctor-assisted suicide should be allowed.

(a) What is the margin of error of the large-sample 99% confidence interval for the proportion of all Quebec adults who would allow doctor-assisted suicide?

(b) How large a sample is needed to get a ±3 percentage point margin of error (this is very commonly used)?

Use the previous sample as a pilot study to get p*. (You may need four decimal places in your critical value to solve this problem.)

1. In a series of projects I determined linear correlation coefficients between various explanatory and response variables. Rank projects thru 5 in order of the increasing strength of correlation.

2. What does r measure?

3. Given the following values of x and y, and using y as the response variable, find the regression line that best fits the data.

4. Estimate the y values associated with an x value of 13

In test of a computer component, it is found that the mean between failures is 520 hours. A modification is made which is supposed to increase the time between failures. Tests on a random sample of 8 modified components resulted in the following times (in hours) between failures. Use a 0.05 significance level to test the claim that the mean time between failures is greater than 520 hours. Assume that the population is normally distributed.

518, 548, 561, 523, 536, 499, 538, 557

a. Compute the mean and standard deviation of the data.

b. State null and alternative hypotheses. Define the parameter.

c. Show the graph and label the p-value in graph.

d. Compare the p-value vs. ?.

e. State the decision and conclusion.

1. A company claims that the mean thermal efficiency of diesel engines produced by them is 32.3%. To test this, claim a random sample of 40 engines were examined which showed the mean thermal efficiency of 31.4% and standard deviation of 1.6%. Can the claim be accepted at 1% level of significance?

2. Answer Both Parts of the question

An industrial designer wants to determine the average amount of time it takes an adult to assemble an “easy to assemble” toy. A sample of 16 times yielded an average time of 19.92 minutes, with a sample standard deviation of 5.73 minutes. Evaluate a 95% confidence interval for the mean assembly time.

How large should a sample be to estimate the population mean μ with α = 0.05, so that the error not exceeds 0.25?

3. Seven students got the following percentage of marks in Chemistry and Physics:

Student

                1              2              3              4              5              6              7

Marks in Chemistry         78           36           98           25           75           82           90

Marks in Physics               84           51           91           60           68           62           86

Calculate the correlation co-efficient for above data.

4. In a study between the amount of rainfall and the quantity of air pollution removed, the in following data were collected

Daily rainfall (x)

(in 0.01 cm)        1.53        1.78        2.60        2.95        3.42

Pollution removed (y) (mg/ m3) 33.50     36.30     40           45.80     53.50

Obtain the line of regression of y on x from the above data. Compute y when x = 3.55

5. Find the coefficient of correlation for the following table:

x: 10       14           18           22           26          30

y: 18       12          24           6              30          36

Is the test statistics is significant using 5% level of significance?

Rosene (1950) studied how quickly hairs on radish roots absorbed water when they were immersed.
For each of eleven radishes, she measured the rate of influx of water for a young root hair and an
old root hair on that radish. The data is given below.
Radish Old Young
A ---------0.89------ 2.13
B -------- 0.49-------1.16
C----------0.91------ 2.60
D----------0.80 ------1.58
E-------- 0.56------ 1.53
F--------- 0.79 -----1.70
G --------0.47------- 2.67
H ---------0.50 ------2.64
I ----------1.08 -------2.19
J---------- 1.65 -------2.54
K ---------1.94 -------4.46
Table 1: Radish root hair absorption data. Rates are in cubic microns per square micron per
minute.
For each pair, the \Young" number is bigger than the \Old" number, so even without a test
it's clear that young roots take in water more quickly. But how much more quickly?
1. Explain what test we should use and why: one sample test, paired samples test or
two independent samples test .
2. (a) Use a normal probability (qqnorm) plot of the di erences (old minus young)
and the sample size to explain why: We should be hesitant to do a t-test on these
di erences (old minus young);
(b) Explain why: We should not take the logs of these di erences (old minus
young.)
3. Instead of using the differences, we can look at the ratio: old divided by young.
This ratio looks to come from a much closer to normal distribution. Write R code to find a
90% con dence interval for the average value of this ratio.

14. A researcher reports outcomes of one-factor ANOVA as F(5, 60) = 3.24, p > .05. Based on the df values, how many groups were compared in the study, and what was the total number of subjects participating in the study?

• A. 6 groups & total of 66 participants.

• B. 4 groups & total of 64 participants.

• C. 5 groups & total of 55 participants.

• D. 4 groups & total of 60 participants.

16. A one-way ANOVA is used to evaluate the mean differences in BMI (i.e., body mass index) between three groups of adults - young adults, middle age adults and elderly. Each age group had n = 10 participants. If the data produced an F-ratio of F = 3.38, which of the following is the correct conclusion from this study (assume p <. 05)?

• A. Reject the null hypothesis and conclude that there are no significant differences in mean BMI.

• B. Fail to reject the null hypothesis and conclude that there are significant differences in mean BMI.

• C. Reject the null hypothesis and conclude that there were significant differences in mean BMI.

• D. Fail to reject the null hypothesis and conclude that there are no significant differences in mean BMI.

17.A one-way ANOVA is used to evaluate the mean differences between five experimental
groups, with n = 12 participants in each group. If the data produce an F= 4.74, which of the following is the correct statistical decision?

• A. Reject the null hypothesis with α = .05 but fail to reject with α = .01.

• B. Reject the null hypothesis with either α = .05 or α = .01.

• C. Fail to reject the null hypothesis with either α = .05 or α = .01.

• D. Reject the null hypothesis with α = .01 but fail to reject with α = .05.

19.

A researcher wanted to examine if the type of music one listens to while studying affects memory performance. She randomly selected five samples of participants and assigned each of them to one of five experimental conditions - listening to classical music, jazz, R&R, R&B or Hip hop. Each sample had 14 subjects (n = 14). All participants were asked to memorize a list of words while listening to one of the five types of music tested. At the end, all participants took a memory test. One-factor ANOVA for independent samples was conducted to test if there is a significant effect of music type on memory performance. The results of the analysis are shown in the following ANOVA summary table.

                                           Source       SS         df        MS             

                           Between Treatments     48       ____     ____    F = 3.00  

                           Within Treatments      ____     ____     ____    

                           Total                        ____     ____

          A. Fill in all missing values in the ANOVA summary table. Show your work (i.e., all computational steps for finding the missing values). Hint: start with the df values and figure out the rest by solving simple equations with one unknown (i.e., refer to the computational formulas for df, MS & F statistic).

           B. Do the data indicate a significant effect of type music on memory performance (assume p < .05)? Use the outcomes of one-factor ANOVA summarized in the table to test this research question.

• the null hypothesis H₀ & the alternative hypothesis H₁ ?
• the critical F used for the decision about H₀ ?
• the decision about H₀?
• if the difference is statistically significant, the effect size, η²?

The number of heads (H) reported by all of you is tabulated below, w here the first column is the number of heads and the second column is the number of times it occurred.

0 0

1 0

2 0

3 2

4 6

5 6

6 9

7 3

8 0

9 1

10 0

The number of tails (T) is simply given by H=10-T. The results of the coin flip can be expresses mathematically in a simple way by assigning the value 1 the n a heads occurs and 0 when a tails occurs. You could choose other numerical assignents, but this one is convenient because the total numerical value is the number of heads obtained in each coin flip experiment.

e) The width of the distribution is given byσ=√Npq. What is it for ourexperiment?

f) Plot the probabilities on the plot you did for part a) usinga suitable over-all normalizing factor to account for the number of people doing the coin flipexperiment.You can find discussions of the binomial function in the manual, Yan’s lectures, and on theweb. If your calculator does not do factorials, you can find web-based ones readily. Showyour calculations to get full credit.

(Note - part a -  Plot the results of this experiment, using H on the x-axis and indicating the expected error (√H)) on each measurement.

g) What fraction of our results for the number of times we observed a numberof heads agrees with the binomial distribution (after you normalize is to ourexperiment) within our estimated errors? We will show laterthat about 2/3 ofthem should.

The average age of online consumers ten years ago was 23.3 years. As older individuals gain

confidence with the Internet, it is believed that the average age has increased. We would like to test

this belief.

(a) Write the appropriate hypotheses to be tested.

(b) The online shoppers in our sample consisted of 40 individuals, had an average age of 24.2

years, with a standard deviation of 5.3 years. What is the test statistic and p‐value for the

hypotheses being tested in part (a)? (Remark: Report the p‐value using the statistical table,

but NOT Excel function.)

(c) What is the practical implication of the conclusion of the hypothesis test at

1.         5% level of significance, and
2.         10% level of significance?

(d) Is our current sample large enough to estimate the mean age of online consumers to be

correct within ±1.5 years at 95% level of confidence? If not, how many additional individuals

need to be selected?