A tire company has developed a new tread design and claim that the newly designed tire has a mean life of 60,000 miles or more.

To examine the claim, a random sample of 16 prototype tires is tested. The mean tire life for this sample is 60,758 miles.

Assume that the tire life is normally distributed with unknown mean µ and standard deviation σ=1500 miles.

(a) Please construct a 90% confidence interval for the mean life of the new designed tire.

Does your confidence interval support the company’s claim?

(b) How would you set up a hypothesis to test the claim?

Please use α=0.05. Is your conclusion consistent with part (a)?

​Historically, the percentage of residents of a certain country who support laws has been 52​%. A recent poll of 987 people showed 531 in favor of laws. Assume the poll was given to a random sample of people. Test the claim that the proportion of those favoring stricter control has changed. Perform a hypothesis​ test, using a significance level of 0.05.

3. A mix beverage machine releases a certain amount of syrup into a chamber where it is mixed with carbonated water. The amount of syrup follows a normal distribution with a mean of 1.29 fl.oz. and a standard deviation 0.016 fl.oz. a. Find the probability that a syrup amount does not exceed 1.33 fl.oz.

b. Find the probability that a syrup amount is less than 1.29 fl.oz.

c. Find the probability that a syrup amount exceeds the mean value by more than two standard deviations.

d. Find the syrup amount so that the probability that it is exceeded is 5%.

1. Economists often track employment trends by measuring the proportion of people who are “underemployed,” meaning they are either unemployed or would like to work full time but are only working part-time. In the summer of 2019, 18.5% of Americans were “underemployed.” The mayor of Detroit wants to show the voters that the situation is not as bad in his city as it is in the rest of the country. His staff takes a simple random sample of 400 Detroit residents and finds that 60 of them are underemployed.  

(a) Does the data give convincing evidence that the proportion of underemployed in Detroit is lower than elsewhere in the country? Perform the appropriate statistical test.

(b) The mayor’s political rival claims that the same poll actually fails to provide sufficient evidence that the underemployment rate in Detroit is any different from the rest of the country. Explain how it is possible for him to come to this conclusion.

(c) Suppose the true underemployment rate in Detroit is actually only 14%. If the mayor were to perform the exact same test again, what is the probability that the mayor’s test results in a Type II Error at the 5% level?

A study asked a random selection of 499 adults from various regions in Israel to complete a survey about whether or not they read while using the toilet. The researchers conducted a test of H0: pi = 0.5 versus Ha: pi ≠ 0.5 where pi is the proportion of adults who read while using the toilet.

a. Use a theory-based method to find the rejection region of the test using a significance level of a = 0.1 and phat as the test statistic. Recall, the rejection region is the set of values of phat that would lead the researchers to reject the null hypothesis.

b. Suppose the true proportion of adults who read while sitting on the toilet is 50%. What is the probability the researchers will incorrectly conclude that the proportion is different from 50%?

c. Suppose the true proportion of adults who read while sitting on the toilet is 55%. Use a theory-based method to calculate the probability the test will reveal that the alternative hypothesis is true.

d. Suppose the researchers were able to collect more data from another 100 adults, so they had a total of 599 adults in their sample. What would happen to the power of the test; would it increase, decrease, or stay the same? Explain.

The selling price of a new car is normally distributed with an average of $21770 and a variance of $5290000.00.

a) What proportion of new cars will sell for more than $19760?
probability =

Is the answer .808914?

b) Assuming a normal distribution, within what selling prices will the middle 83% fall?
lower =  , upper =

could I see the work out for part b? thank you

Note: Do NOT input probability responses as percentages; e.g., do NOT input 0.9194 as 91.94.

11_ The average weight of 40 randomly selected minivans was 4150 pounds. The standard deviation was 480 pounds. Find the 99% confidence interval of the true mean weight of the minivans.

What is the standard error for step1? What is the Z or t score for step 2? What is the confidence interval (Step 3)

Is college worth it? Among a simple random sample of 344 American adults who do not have a four-year college degree and are not currently enrolled in school, 155 said they decided not to go to college because they could not afford school.

1. Calculate a 90% confidence interval for the proportion of Americans who decide to not go to college because they cannot afford it, and interpret the interval in context. Round to 4 decimal places. ( 0.4383 , 0.5269 )

2. Suppose we wanted the margin of error for the 90% confidence level to be about 3.5%. What is the smallest sample size we could take to achieve this? Note: For consistency's sake, round your z* value to 3 decimal places before calculating the necessary sample size. Choose n = 1335

In the course of the thesis work, a student develops a new approach for the solution of a problem (here referred to as method B). The current state-of-the-art approach, method A, is well published in the literature and has been applied to a large standard problem set where its average performance was discovered to be (and published in the main paper by the developers as) 7 with a standard deviation of 3 across the different problems in the problem set. In addition to the publication, the developers of method A also provide their code for anyone to be able to experiment with and the student decides to pick a random set of 15 problems from the standard problem set and apply both methods to these problems, resulting in the following performance numbers for method A: {8, 3, 10, 8, 11, 4, 6, 4, 12, 4, 5, 10, 6, 2, 10}, and the following performance numbers for the student’s method B: {9, 5, 9, 10, 15, 4, 7, 4, 12, 7, 8, 10, 6, 4, 12}. Looking at this data, the student discovers that it seems that method B outperforms method A and sets out to prove this using significance testing with a two-tailed 5% significance threshold. Given that both published performance results as well as the student’s experimental results are available, a number of tests can be performed.

Evaluate the results in terms of the hypothesis that method B has a higher performance than method A. List all the steps (and formulas) involved in the test and what the result implies for the significance of the hypothesis.

In the town of Maplewood a certain type of DVD player is sold at just two stores. 38% of the sales are from store A and the rest of the sales are from store B. 7% of the DVD players sold at store A are defective while 3% of the DVD players sold at store B are defective. If Kate receives one of these DVD players as a gift and finds that it is defective, what is the probability that it came from store A? Express your answer as a percentage rounded to the nearest hundredth.

A class survey in a large class for first-year college students asked, "About how many minutes do you study on a typical weeknight?" The mean response of the 261 students was x¯¯¯x¯ = 130 minutes. Suppose that we know that the studey time follows a Normal distribution with standard deviation σσ = 65 minutes in the population of all first-year students at this university. Regard these students as an SRS from the population of all first-year students at this university. Does the study give good evidence that students claim to study more than 2 hours per night on the average?

(a) State null and alternative hypotheses in terms of the mean study time in minutes for the population.
(b) What is the value of the test statistic z?
(c) Can you conclude that students do claim to study more than two hours per weeknight on the average?

(a) H0:  Ha:  (Type in "mu" as the substitute for μμ and "!=" for ≠≠.)
(b) z:
(c) Conclusion:  (Answer with "Yes/Y" or "No/N".)

A study is conducted to determine if a newly designed text book is more helpful to learning the material than the old edition. The mean score on the final exam for a course using the old edition is 75. Ten randomly selected people who used the new text take the final exam. Their scores are shown in the table below.

Use a 0.010.01 significance level to test the claim that people do better with the new edition. Assume the standard deviation is 10.3. (Note: You may wish to use statistical software.)

(a) What kind of test should be used?

A. Two-Tailed
B. One-Tailed
C. It does not matter.

(b) The test statistic is  (rounded to 2 decimals).

(c) The P-value is

(d) Is there sufficient evidence to support the claim that people do better than 75 on this exam?

A. Yes
B. No

(e) Construct a 9999% confidence interval for the mean score for students using the new text.
<μ<<μ<

The next three questions relate to the following situation:

A randomised experiment was conducted by randomly assigning each participant to either walk for half an hour three times a week or to sit quietly and read a book for half an hour three times a week. At the end of a year the change in participant's blood pressure was measured, and the change was compared for the two groups.

please answer these two quetions

1153 – Chapter 12 & 5 HW Questions 1. ACT scores follow an approximately normal distribution. One year, the mean score was 18.2 with standard deviation 5.8. Round proportions to 4 decimal places and scores to the appropriate integer. (a) What proportion of students scored below 20? Above 25? Between 20 and 30? (b) What score did someone at the 80th percentile have? (c) Describe the top 10% of ACT scores: (d) Describe the middle 50% of ACT scores:

2. At a zoo, Biteyfloofers have a mean length of 11” and standard devation 2.5”, while Fluffersnappers have a mean length of 10” and standard deviation 2”. Both follow an approx. normal distribution. (a) Which is more unusual, a Fluffersnapper that is 12” long or a Biteyfloofer that is 12”? (b) Which would seem longer relative to their populations, a 9” Fluffersnapper or a 9.5” Biteyfloofer? (c) Use the empirical rule to compare the middle 95% of heights for each creature.

3. For each situation, decide if it would be reasonable to use the normal distribution to describe the sampling distribution. Supply a brief explanation for each. (a) A polling company takes a SRS of 1000 voters and calculates the proportion who plan to vote in favor of Proposition 60. Previous polls suggest 26% are in favor of Prop. 60. (b) Brian rolls a fair 6-sided die 50 times and records the number of times “2” comes up.

4. A 2011 Gallup poll found that 76% of Americans believe that high achieving high school students should be recruited to become teachers. This poll was based on a random sample of 1002 Americans. (a) Find a 90% confidence interval for the proportion of Americans who would agree with this. (b) Interpret your interval in this context. (c) Explain what “90% confidence” means in this context. (d) Do these data refute a pundit’s claim that at least 2/3 of Americans believe this statement. Explain.

5. A 95% confidence interval for a politician’s level of support is given by (0.29, 0.46). Which is correct? Why? (a) There’s a 95% chance that the interval correctly captured the politician’s level of support for those sampled, i.e. that between 29% and 46% of the sample support the politician. (b) 95% of all samples will produce values between 29% and 46%. (c) There’s a 95% chance that the interval correctly captured the politician’s level of support, i.e. that between 29% and 46% of the constituents support the politician. (d) 95% of the time, between 29% and 46% of constituents will support the politician.

6. For each scenario, indicate if the chapter 13 confidence interval is appropriate, and briefly explain why. (a) A prison has records on all 385 of its inmates, and finds that 59% have been vaccinated against pararibulitis. (b) A random sample of 1178 inmates in prisons across Oklahoma finds that 59% have been vaccinated against pararibulitis. (Note: Oklahoma has more than 62,000 inmates) (c) A prison doctor notes that, of the last 86 inmates to receive medical care, 59% have been vaccinated against pararibulitis.

Follow the directions for the common assessment in Hypothesis Testing. The complete solution must include all the steps in hypothesis testing.

Identify the null and alternative hypothesis, calculate the test statistic, along with the P-value. Write the conclusion about the null hypothesis and the final conclusion in context of the problem.

1. The maximum acceptable level of a certain toxic chemical in vegetables is been set at 0.4 parts per million(ppm). A consumer health group measured the level of the chemical in a random sample of tomatoes obtained from one producer. The levels is ppm are shown in the table below:

Do the data provide sufficient evidence to support the claim that the mean level of the chemical in tomatoes from this producer is greater than the recommended level of 0.4 ppm? Use a 0.05 significance level to test the claim that these sample levels come from a population with a mean greater than 0.4 ppm. Use the P-value method of testing the hypothesis. Assume that the standard deviation of levels of the chemicals in all such tomatoes is 0.21 ppm.

11.30  A simpler model. In the multiple regression analysis using all four explanatory variables, Theaters and Budget appear to be the least helpful (given that the other two explanatory variables are in the model).

1. (a) Perform a new analysis using only the movie’s opening-weekend revenue and IMDb rating. Give the estimated regression equation for this analysis.

2. (b) What percent of the variability in USRevenue is explained by this model?

3. (c) Test the null hypothesis that Theaters and Budget combined add no additional predictive information beyond what is already contained in Opening and Opinion?

All Data required is BELOW: