A company is developing a new high performance wax for cross country ski racing. In order to justify the price marketing​ wants, the wax needs to be very fast.​ Specifically, the mean time to finish their standard test course should be less than 55 seconds for a former Olympic champion. To test​ it, the champion will ski the course 8 times. The​ champion's times​ (selected at​ random) are

58.9​,

64.3​,

45.6​,

52.1​,

45.2​,

49.9​,

54.9​,

and

44.3

seconds to complete the test course. Should they market the​ wax? Assume the assumptions and conditions for appropriate hypothesis testing are met for the sample. Use 0.05 as the​ P-value cutoff level.

Calculate the​ P-value.

​P-value=

An institute reported that 60​% of its members indicate that lack of ethical culture within financial firms has contributed most to the lack of trust in the financial industry. Suppose that you select a sample of 100 institute members.

b. The probability is 90​% that the sample percentage will be contained within what symmetrical limits of the population​ percentage? The probability is 90​% that the sample percentage will be contained above nothing​% and below nothing​%.

Although studies continue to show smoking leads to significant health problems, 20% of adults in the United States smoke. Consider a group of 280 adults.

If required, round your answers to four decimal places.

a. What is the expected number of adults who smoke?

b. What is the probability that fewer than 40 smoke?

c. What is the probability that from 35 to 70 (inclusive) smoke?

d. What is the probability that 70 or more smoke?

Construct a confidence interval of the population proportion at the given level of confidence.

x equals=860​,

n equals=1200​,

90​% confidence

What are the upper and lower bounds

The Crown Bottling Company has just installed a new bottling process that will fill 16-ounce bottles of the popular Crown Classic Cola soft drink. Both overfilling and underfilling bottles are undesirable: Underfilling leads to customer complaints and overfilling costs the company considerable money. In order to verify that the filler is set up correctly, the company wishes to see whether the mean bottle fill, μ, is close to the target fill of 16 ounces. To this end, a random sample of 31 filled bottles is selected from the output of a test filler run. If the sample results cast a substantial amount of doubt on the hypothesis that the mean bottle fill is the desired 16 ounces, then the filler’s initial setup will be readjusted. (a) The bottling company wants to set up a hypothesis test so that the filler will be readjusted if the null hypothesis is rejected. Set up the null and alternative hypotheses for this hypothesis test. H0 : μ 16 versus Ha : μ 16 (b) Suppose that Crown Bottling Company decides to use a level of significance of α = 0.01, and suppose a random sample of 31 bottle fills is obtained from a test run of the filler. For each of the following four sample means— x⎯⎯ = 16.05, x⎯⎯ = 15.98, x⎯⎯ = 16.03, and x⎯⎯ = 15.90 — determine whether the filler’s initial setup should be readjusted. In each case, use a critical value, a p-value, and a confidence interval. Assume that σ equals .1. (Round your z to 2 decimal places and p-value to 4 decimal places and CI to 3 decimal places.) x⎯⎯ = 16.05 z p-value CI [ , ] x⎯⎯ = 15.98 z p-value CI [ , ] x⎯⎯ = 16.03 z p-value CI [ , ] x⎯⎯ = 15.90 z p-value CI [ , ]

Give and example of a real life situation that includes: DATA STATISTIC PARAMETER How does the statistic and the parametere differ?

Based on experience, you believe that less than 15% of the population of your city dislike the taste of cilantro. Two-hundred people were randomly selected from your city and questioned about their like or dislike of the taste of cilantro. Thirty-two of those questioned stated they disliked the taste of cilantro.

Complete the tasks and answer the questions.

• Use the 2SD method to estimate the true proportion of the population of your city that dislikes the taste of cilantro. State the resulting confidence interval in both forms – the interval notation and the sample proportion ± the margin of error notation.
• Write the interpretation of this confidence interval.
• Use the theory-based method to estimate the true proportion of the population of your city that dislikes the taste of cilantro with a 95% confidence interval. State the resulting confidence interval in both forms – the interval notation and the sample proportion ± the margin of error notation.
• Write the interpretation of this confidence interval.
• Use the theory-based method to estimate the true proportion of the population of your city that dislikes the taste of cilantro with an 88% confidence interval. State the resulting confidence interval in both forms – the interval notation and the sample proportion ± the margin of error notation.
• Write the interpretation of this confidence interval.

In a random sample of 88 ears of corn, farmer Carl finds that 9 of them have worms. He wants to find the 99% confidence interval for the proportion of all his corn that has worms.

(a) What is the point estimate for the proportion of all of Carl's corn that has worms? Round your answer to 3 decimal places.

(b) What is the critical value of z (denoted zα/2) for a 99% confidence interval? Use the value from the table or, if using software, round to 2 decimal places. zα/2 =

(c) What is the margin of error (E) for a 99% confidence interval? Round your answer to 3 decimal places. E =

(d) Construct the 99% confidence interval for the proportion of all of Carl's corn that has worms. Round your answers to 3 decimal places. < p <

(e) Based on your answer to part (d), are you 99% confident that less than 22% of Carl's corn has worms?

No, because 0.22 is above the upper limit of the confidence interval.

Yes, because 0.22 is below the upper limit of the confidence interval.

Yes, because 0.22 is above the upper limit of the confidence interval.

No, because 0.22 is below the upper limit of the confidence interval. Additional Materials

SOLVE WITH SPSS ONLY

We wish to assess the effect of three different track surfaces on sprinter speed. Six world-class sprinters are asked to run five 100m dashes on each of the three track surfaces. Their average times are recorded below. USE SPSS NO EXCEL NO HAND

Surface 1 Surface 2 Surface 3

Sprinter 1 9.85 10.00 10.04

Sprinter 2 9.90 10.07 10.16

Sprinter 39.89 9.99 10.17

Sprinter 4 9.88 9.98 10.04

Sprinter 5 9.81 10.03 10.10

Sprinter 6 9.81 9.95 10.12

Using the sprinters as blocks, discuss the differences between the track surfaces as suggested by SPSS. Give a statement to be tested, identify the random variables involved and the assumptions you make about them, state the hypotheses to be tested, ask SPSS to run the analysis for you, including a post hoc, and then discuss the outcome. Describe the critical region(s) upon which you base your decisions. Include any SPSS output in your discussion.

Almost all medical schools in the United States require students to take the Medical College Admission Test (MCAT). To estimate the mean score μ of those who took the MCAT on your campus, you will obtain the scores of an SRS of students. The scores follow a Normal distribution, and from published information you know that the standard deviation is 10.4 . Suppose that, unknown to you, the mean score of those taking the MCAT on your campus is 495 .

In answering the questions, use z‑scores rounded to two decimal places.

(a) If you choose one student at random, what is the probability that the student's score is between 490 and 500 ? Use Table A, or software to calculate your answer.

(Enter your answer rounded to four decimal places.)

probability:

(b) You sample 25 students. What is the standard deviation of the sampling distribution of their average score ?¯? (Enter your answer rounded to two decimal places.)

standard deviation:

(c) What is the probability that the mean score of your sample is between 490 and 500 ? (Enter your answer rounded to four decimal places.)

probability:

STATE: How heavy a load (in pounds) is needed to pull apart pieces of Douglas fir 44 inches long and 1.51.5 inches square? Given are data from students doing a laboratory exercise.

To access the complete data set, click the link for your preferred software format:

Excel  Minitab  JMP  SPSS TI  R  Mac-TXT   PC-TXT  CSV CrunchIt!

We are willing to regard the wood pieces prepared for the lab session as an SRS of all similar pieces of Douglas fir. Engineers also commonly assume that characteristics of materials vary Normally. Suppose that the strength of pieces of wood like these follows a Normal distribution with standard deviation 3000 pounds.

PLAN: We will estimate μ by giving a 90% confidence interval.

SOLVE: Find the sample mean ?¯ . (Enter your answer rounded to the nearest whole number.)

?¯=

Give a 90% confidence interval, [low,high] , for the mean load required to pull the wood apart. (Enter your answers rounded to the nearest whole number.)

???=

ℎ??ℎ=

Part I: Between-Groups Design

In the between-groups design, researchers were interested in whether cholesterol levels would differ depending on diet. Twenty participants were randomly assigned to one of two different groups. Group A was assigned a diet rich in fruits and vegetables and with no trans fats. Group B participants were asked to follow their normal diets, which contained varying levels of trans fats depending on the individual. After one month, blood samples were drawn and the following levels of cholesterol were obtained:

In 2 to 3 sentences in a Microsoft Word document, answer the following questions:

• What is the independent variable in this study?
• What are the levels of that independent variable?
• What is the dependent variable?

Part II: Within-Subjects Design

In the within-subjects design, researchers were interested in whether participants could lower their cholesterol levels by changing from a diet higher in trans fats to one with no trans fats. Ten research participants were selected. A baseline measure of cholesterol was taken from each. They were then put on a diet rich in fruits and vegetables and devoid of trans fats for one month. At the end of that month, blood cholesterol was again measured and the following results were obtained:

In 2 to 3 sentences in a Microsoft Word document, answer the following questions:

• What is the independent variable in this study?
• What are the levels of that independent variable?
• What is the dependent variable?

6. It's presidential primary season and canvassers are out talking to voters. In a city that's known to have 20% registered republicans, 5 canvassers each go to 50 randomly selected homes to ask about voting preferences. Amazingly, every home has someone willing to talk. Which of the following is the most plausible sequence of republican voters met by these canvassers?

a. 5%, 80%, 65%, 8%, 70%

b. they're all equally plausible

c. 15%, 25%, 22%, 28%, 20%

d. 20%, 20%, 20%, 20%, 20%

7.

The average birthweight of babies in Oregon is 3500 grams with a standard deviation of 500 grams. You collected 100 samples of 100 babies and calculated the mean weight of each of the samples. You then graph the means that you've calculated. What does your distribution of sample means look like?

a. it's pretty normal

b. it has no particular shape

c. it's skewed either left or right

8.

Still thinking about your distribution of the samples of baby weights, what would the standard deviation of your 100 sample means be?

a. more than 500 grams

b. not enough information to know

c, less than 500 grams

d. same as the population, 500 grams

Hypothesis testing terminology

Match each of the following descriptions with its corresponding term from the list above. Enter the letter corresponding to the correct term in the blank.

Examples, please

Paired design with repeated measures

Paired design with matched pairs

At a recent halloween party, the women appeared to be consuming more packages of halloween candy than were the men. If the mean number of packages consumed by the 3 men was 4, and that for the 7 women was 6, and the standard deviation for the whole group was 2 packages, what was the correlation between gender and the number of packages consumed?

I am having difficulties understanding how to solve this homework problem.