17) On this worksheet, make an XY scatter plot linked to the following data:

18) Add trendline, regression equation and r squared to the plot.

Add this title. ("Scatterplot of X and Y Data")

19)

A manufacturer of automobile batteries claim that at least 80% of the batteries
that it produces will last 36 months. A consumers’ advocate group wants to evaluate this
longevity claim and selects a random sample of 28 batteries to test. The following data indicate
the length of time (in months) that each of these batteries lasted (i.e., performed properly
before failure): 42.3, 39.6, 25.0, 56.2, 37.2, 47.4, 57.5, 39.3, 39.2, 47.0, 47.4, 39.7, 57.3, 51.8,
31.6, 45.1, 40.8, 42.4, 38.9, 42.9, 34.1, 49.0, 41.5, 60.1, 34.6, 50.4, 30.7, 44.1. Now, we would
like to test, at a significance level of 0.05, if there is a significant evidence that less than 80%
of the batteries will last at least 36 months? Conduct and conclude the test.

I am very confused about how to find the critical value of the test statistic.

I have found the test statistic of 5.636, with 1% significance level and two degrees of freedom. How do I calculate the critical value?

Urban traffic congestion throughout the world has been increasing in recent​ years, especially in developing countries. The accompanying table shows the number of minutes that randomly selected drivers spend stuck in traffic in various cities on both weekdays and weekends. Complete parts a through e below.

a) Using alpha = 0.05​, is there significant interaction between the city and time of the​ week?

Identify the hypotheses for the interaction between the city and time of the week. Choose the correct answer below.

A. H0​: City and time of the week do not​ interact, H1​: City and time of the week do interact

B. H0​: μCity ≠ μTime​, H1​: City=μTime

C. H0​: μCity=μTime​, H1​: μCity≠μTime

D. H0​: City and time of the week do​ interact, H1​: City and time of the week do not interact

Find the​ p-value for the interaction between city and time of the week.

​p-value=????

​(Round to three decimal places as​ needed.)

Draw the appropriate conclusion for the interaction between the city and time of the week. Choose the correct answer below.

A. Do not reject the null hypothesis. There is insufficient evidence to conclude that the city and time of the week interact.

B. Do not reject the null hypothesis. There is insufficient evidence to conclude that the means differ.

C. Reject the null hypothesis. There is insufficient evidence to conclude that the means differ.

D. Reject the null hypothesis. There is sufficientevidence to conclude that the city and time of the week interact.

​b) Using​ two-way ANOVA and α​=0.05​,does the city have an effect on the amount of time stuck in​ traffic?

Identify the hypotheses to test for the effect of the city. Choose the correct answer below.

A. H0​: μCity A=μCity B=μCity C=μCity D​, H1​: Not all city means are equal

B. H0​: μCity=μTime​, H1​: μCity≠μTime

C. H0​: μCity A≠μCity B≠μCity C≠μCity D​, H1​: μCity A=μCity B=μCity C=μCity D

D. H0​: μCity A=μCity B=μCity C=μCity D​, H1​: μCity A>μCity B>μCity C>μCity D

Find the​ p-value for the effect of the city.

​p-value=???

​(Round to three decimal places as​ needed.)

Draw the appropriate conclusion for the effect of the city. Choose the correct answer below.

A. Reject the null hypothesis. There is sufficient evidence to conclude that not all city means are equal.

B. Do not rejectthe null hypothesis. There is sufficient evidence to conclude that the means differ.

C. Do not rejectthe null hypothesis. There is insufficient evidence to conclude that not all city means are equal.

D. It is inappropriate to analyze because the city and the time of the week interact.

​c) Using​ two-way ANOVA and α​=0.05​, does the time of the week have an effect on the amount of time stuck in​ traffic?

Identify the hypotheses to test for the effect of the time of the week. Choose the correct answer below.

A.H0​: μWeekday=μWeekend​, H1​: Not all time of the week means are equal

B. H0​: μCity=μTime​, H1​:μCity≠μTime

C. H0​: μCity A=μCity B=μCity C=μCity D​, H1​: Not all time of the week means are equal

D. H0​: μWeekday≠μWeekend​, H1​:μWeekday=μWeekend

Find the​ p-value for the effect of the time of the week.

​p-value=???

​(Round to three decimal places as​ needed.)

Draw the appropriate conclusion for the effect of the time of the week. Choose the correct answer below.

A. Do not reject the null hypothesis. There is insufficient evidence to conclude that not all time of the week means are equal.

B. Do not reject the null hypothesis. There is sufficient evidence to conclude that the means differ.

C. Reject the null hypothesis. There is sufficient evidence to conclude that not all time of the week means are equal.

D. It is inappropriate to analyze because the city and the time of the week interact.

​

d) Are the means for weekdays and weekends significantly​different?

A. Yes​,because there is insufficient evidence to conclude that not all time of the week means are equal.

B. No​, because there is insufficient evidence to conclude that not all time of the week means are equal.

C.Yes​, because there is sufficient evidence to conclude that not all time of the week means are equal.

D. The comparison is unwarranted because the city and the time of the week interact.

Blood cocaine concentration (mg/L) was determined both for a sample of individuals who had died from cocaine-induced excited delirium (ED) and for a sample of those who had died from a cocaine overdose without excited delirium; survival time for people in both groups was at most 6 hours. The accompanying data was read from a comparative boxplot in an article.

(a)

Determine the median, fourths, and fourth spread for the ED sample.

medianlower fourthupper fourthfourth spread

Determine the median, fourths, and fourth spread for the Non-ED sample.

medianlower fourthupper fourthfourth spread

Simple regression was employed to establish the effects of childhood exposure to lead. The effective sample size was about 122 subjects. The independent variable was the level of dentin lead (parts per million). Below are regressions using various dependent variables.

(a) Calculate the t statistic for each slope, at significance level = 0.01. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)
  

Activity 3: Which procedure?
For each question, determine which inference procedure is appropriate (perform hypothesis test or construct a confidence interval), and identify the parameter of interest (p, p1 – p2, µ, µ1 – µ2, µd).
What percentage of college students engage in underage drinking in their freshman year?

Test or Interval Parameter

What is the average change in a person’s heart rate when comparing measurements from before and after a scary scene in a horror film?

Test or Interval Parameter

What is the average number of siblings of all Penn State students?

Test or Interval Parameter

Is there a difference in the percent of college freshman and college sophomores who engage in underage drinking?
Test or Interval Parameter

On average, are college graduates exiting school with a GPA above 3.0?

Test or Interval Parameter

Is the percent of sophomores living on campus at Penn State different than 30%?
Test or Interval Parameter

Is there a difference in the percentage of season games of their favorite sport a fan attends based on if their favorite sport is baseball or basketball?

Test or Interval Parameter

write three benefits from doing the principle component analysis?

You have prepared 10 types of treats for your 5 cats. You don’t know which treat each of your cats will

go for, so you have bought for each type enough treats for all your cats. Assume that each cat is equally

likely to choose any type of treats, and let X be the number of pairs of cats that will choose the same

type of treats. Compute E(X) and Var(X).

(Hint: consider events Ai,j that the ith and jth cats will choose the same type of treats.)

1. A researcher wishes to see whether there is any difference in the weight gains of athletes following one of three special diets. Athletes are randomly assigned to three groups and placed on the diet for 6 weeks. The weight gains (in pounds) are shown here. At α = 0.05, can the researcher conclude that there is a difference in the diets?

Diet A             Diet B             Diet C             Total

                        3                      10                   8

6                      12                   3

7                      11                   2

4                      14                   5

                                    8

                                    6

the critical value = 3.98

Conclusion:

Analysis of Variance Summary Table

P-value

Source                             Sum of Squares       D.F.    Mean Square F ratio p-value

Between groups                      

Within                            

SSB                                                           SSW   

MSB = SSBk-1                                               MSW=SSWN-k

F = MSBMSW

ANOVA 1 TUKEY B

                                    ID         N

                                    ____________________________

                                    3           4       4.50

                                        ____________________________

                                    1          4          5.00             

                                    ____________________________

                                    2          6                                  10.17

                                    _____________________________

                                    Sig.                 .954               1.00

1. A regular type of laminate is currently being used by a manufacturer of circuit boards. A special laminate has been developed to reduce warpage.   The regular laminate will be used on one sample of circuit boards and the special laminate on another independent sample of circuit boards. The amount of warpage will then be determined for each circuit board. The manufacturer will then switch to the special laminate only if it can be demonstrated that the true average amount of warpage for that laminate is less than for the regular laminate. State the relevant hypotheses, and describe the type I and type II errors in the context of this scenario.

2. The measured residual flame time, in seconds, for strips of treated children’s nightwear are given in the following table.

        Suppose a true average flame time of at most 9.75 seconds had been mandated. Does the data suggest that this condition has not been met? Carry out an appropriate test after first investigating the plausibility of assumptions that underlie your method of inference. Use the recommended sequence of steps and reach a conclusion using a significance level of 0.01:

a. Identify the parameter of interest and describe it in the context of the problem situation:

b. Determine the null value and state the null hypothesis:

c. State the appropriate alternative hypothesis:

d. Give the formula for the computed value of the test statistic (substituting the null value and the known values of any other parameters, but not those of any sample-based quantities):

e. Compute any necessary sample quantities, substitute into the formula for the test statistic value and compute that value:

f. Determine the P-value:

g. Compare the selected or specified significance level to the P-value to decide whether H₀ should be rejected, and state this conclusion in the problem context:

1) Of all the trees planted by a landscaping firm, 10% survive. What is the probability that 7 or more of the 9 trees they just planted will survive? (Use a table of binomial probabilities. Give your answer correct to four decimal places.)

2)

Find the following probabilities for X = pulse rates of group of people, for which the mean is 78 and the standard deviation is 4. Assume a normal distribution. (Round all answers to four decimal places.)

(a) P(X ≤ 75).


(b) P(X ≥ 84).


(c) P(68 ≤ X ≤ 86).

1. Suppose that you are interested in determining whether the advice given by a physician during a routine physical examination is effective in encouraging patients to stop smoking. In a study of current smokers, one group of patients was given a brief talk about the hazards of smoking and was encouraged to quit. A second group received no talk related to smoking. All patients were given a follow-up exam. In the sample of 150 patients who had received the talk, 23 reported that they had quit smoking. In the sample of 90 patients that hadn’t received a talk 8 had ceased smoking.

a. Create a 2x2 table based on the data provided in the question.

b. Use Chi-square test to determine whether there is an association between receiving talks and quitting smoking. Choose α = 0.05.

A sample of 1100 computer chips revealed that 58% of the chips fail in the first 1000 hours of their use. The company's promotional literature claimed that less than 61% fail in the first 1000 hours of their use. Is there sufficient evidence at the 0.01 level to support the company's claim?

State the null and alternative hypotheses for the above scenario.

In a study, 1319 schoolchildren at the age of 12 were random selected to be questioned on the prevalence of symptoms of severe cold. Another 1319 schoolchildren at age 14 were random selected to be questioned on the prevalence of symptoms of severe cold. For schoolchildren of age 12, 356 children were reported to have severe colds in the past 12 months, for schoolchildren of age 14, 468 were reported to have severe colds in the past 12 months. Is there an association between the prevalence of severe cold and the age of 12 and 14?

Please conduct a hypothesis testing using the Chi-square test to justify your conclusion.