Slices of pizza for a certain brand of pizza have a mass that is approximately normally distributed with a mean of 67.3 grams and a standard deviation of 2.01 grams. a) For samples of size 22 pizza slices, what is the standard deviation for the sampling distribution of the sample mean? b) What is the probability of finding a random slice of pizza with a mass of less than 66.8 grams? c) What is the probability of finding a 22 random slices of pizza with a mean mass of less than 66.8 grams? d) What sample mean (for a sample of size 22) would represent the bottom 15% (the 15th percentile)? in grams

1. The amount of time a tire lasts is normally distributed with a mean of 30,000 km and standard
deviation of 2000 km.
(a) 68% of all tires will last between ____________ km and _____________ km.
(b) 95% of all tires will last between ____________ km and _____________ km.
(c) What percent of the tires will have a life that exceeds 26,000 km? _________
(d) What percent of the tires will have a life that lasts between 28,000 and 34,000 km? ______
(e) If a company purchases 2000 tires, how many tires are expected to last
 more than 28,000 km? ___________
 between 24,000 and 32,000 km? ____________

A series of experiments was conducted to measure bubble diameter. Three characteristics x1, x2, and x3 were varied for each experiment. The data obtained are listed in the below table.

1. Consider the multiple regression model that relates bubble diameter to x1, x2, and x3.
2. What would be the bubble diameter for x1=5.9, x2 =0.9, and x3=11.5

Question 1:
Given the following probability distribution for a random variable X: x P(X=x)
-2
0.30
-1
0.15
0
0.20
1
0.20
2
0.15
a) Explain two reasons why the above distribution is a valid probability distribution.
b) Calculate μX and σX.
c) Determine the cdf(X), and write it as an additional column in the table.
d) Calculate P(−1<X≤3) .
e) Draw a histogram that represents the probability distribution of X.

To assess the accuracy of a laboratory scale, a standard weight known to weigh 10 grams is weighed repeatedly. The scale readings are normally distributed with unknown mean (this mean is 10 grams if the scale has no bias). The standard deviation of the scale readings is known to be 0.0003 gram.

(a) The weight is measured three times. The mean result is 10.0023 grams. Give a 98% confidence interval for the mean of repeated measurements of the weight. (Round your answers to four decimal places.)

(b) How many measurements must be averaged to get a margin of error of ±0.0001 with 98% confidence? (Round your answer up to the nearest whole number.)

EPA regulates the level of CO2 emissions. Recently, the EPA began applying an automated control chart methodology to detect undermeasurement of emissions data. The three daily samples of CO2 levels for each of 15 days are shown in the below table.

a. Construct two control charts for the daily average and variation of CO2 levels.

b. Based on the control chart, describe the behavior of the measurement process.

In August in September 2005, hurricanes Katrina and Rita caused extraordinary flooding in New Orleans, Louisiana. Many homes were severely damaged or destroyed, and of those that survived, many required extensive cleaning. It was thought that cleaning flood-damaged homes might present a health hazard due to the large amount of mold present in many of the homes. In a sample of 365 residents of Orleans Parish who had participated in the cleaning of one or more homes, 77 had experienced symptoms of wheezing, and in a sample of 179 residents who had not participated in cleaning, 23 reported wheezing symptoms. Can you conclude that the proportion of residents with wheezing symptoms is greater among those who participated in the cleaning of flood-damaged homes?

a. State whether the test is:

i) a two-sample t-test (independent samples)

ii) a matched pairs

iii) a two sample proportion test

b. Write H0 and H1

c. Using Minitab, list the test statistic the p-value your conclusion: reject H0 or do not reject H0. Note: if α is not provided, use a 0.05 significance level

d.   Write a sentence that explains your conclusion in context with the claim. Include the significance level and p-value in this sentence.

e.   Copy and paste the relevant Minitab output into the document. Answers alone are sufficient, you do not need to copy the exercise into the document.

A crossover trial is a type of experiment used to compare two drugs. Subjects take one drug for a period of time, then switch to the other. The responses of the subjects are then compared using matched-pair methods. In an experiment to compare two pain relievers, seven subjects took one pain reliever for two weeks, then switched to the other. They rated their pain level from 1 to 10, with larger numbers representing higher levels of pain. Can you conclude that the main pain level is less with drug B? Use α = 0.05.

a. State whether the test is:

i) a two-sample t-test (independent samples)

ii) a matched pairs

iii) a two sample proportion test

b. Write H0 and H1

c. Using Minitab, list the test statistic the p-value your conclusion: reject H0 or do not reject H0. Note: if α is not provided, use a 0.05 significance level

d.   Write a sentence that explains your conclusion in context with the claim. Include the significance level and p-value in this sentence.

e.   Copy and paste the relevant Minitab output into the document. Answers alone are sufficient, you do not need to copy the exercise into the document.

An experiment was run to determine whether four specific firing temperatures affect the density of a certain type of brick. The following data was collected.

Set up a regression model to describe the experiment. State the model and all assumptions, interpret the meaning of each parameter. Show all the steps needed to estimate all model parameters, including writing down the X matrix and the Y vector. Can you estimate the value of β0?

In a random sample of 340 cars driven at low altitudes, 46 of them exceeded a standard of 10 grams of particulate pollution per gallon of fuel consumed. In an independent random sample of 85 cars driven at high altitudes, 21 of them exceeded the standard. Can you conclude that the proportion of high altitude vehicles exceeding the standard is greater than the proportion of low altitude vehicles exceeding the standard?

a. State whether the test is:

i) a two-sample t-test (independent samples)

ii) a matched pairs

iii) a two sample proportion test

b. Write H0 and H1

c. Using Minitab, list the test statistic the p-value your conclusion: reject H0 or do not reject H0. Note: if α is not provided, use a 0.05 significance level

d.   Write a sentence that explains your conclusion in context with the claim. Include the significance level and p-value in this sentence.

e.   Copy and paste the relevant Minitab output into the document. Answers alone are sufficient, you do not need to copy the exercise into the document.

The incidence of a deadly disease, among a certain population, is 0.01%. Individuals, randomly selected from this population are submitted to a test whose accuracy is 99% both ways. That is to say, the proportion of positive results among people known to be affected by the disease is 99%. Likewise, testing people that are not suffering from the disease yields 99% negative results. The test gives independent results when repeated. An individual test positive.

a) What is the probability that this person is actually affected?

b) How much more likely are they to have SIDA if they test positive? How likely overall are they if they test positive?

c) The test is repeated twice. What is the probability that the person has SIDA if all three tests are positive? If the first is positive and the next two tests are negative?

Researchers have been studying the association between cigarette smoking and caffeine intake and

Parkinson's Disease for more than 40 years. The results of a study by Checkoway et al. (2002) follow:

Ever having smoked cigarettes resulted with an odds ratio (OR) = 0.5 (95% confidence interval (CI):

0.4, 0.8).

The OR for current smokers was OR = 0.3 (95% CI: 0.1, 0.7).

Among ex-smokers the OR = 0.6 (95% CI: 0.4, 0.9).

Interpret the three ORs (in your own words).

The effect of phosphate supplementation on bone formation was assessed in six healthy dogs. For each dog, bone formation was measured for a 12-week period of phosphate supplementation as well as for a prior 12-week control period.

Test the claim that there is a significant difference in bone formation between the control time period and the phosphate supplementation time period. Use α = 0.10.

a. State whether the test is:

i) a two-sample t-test (independent samples)

ii) a matched pairs

iii) a two sample proportion test

b. Write H0 and H1

c. Using Minitab, list the test statistic the p-value your conclusion: reject H0 or do not reject H0. Note: if α is not provided, use a 0.05 significance level

d.   Write a sentence that explains your conclusion in context with the claim. Include the significance level and p-value in this sentence.

e.   Copy and paste the relevant Minitab output into the document. Answers alone are sufficient, you do not need to copy the exercise into the document.

Current estimates are that somewhere between 1% and 5% of the U.S. population hasbeen infected with Covid-19. A serological test for Covid-19 is supposed to determine if a personhas antibodies for that virus, which would indicate a previous infection. Some claim that if a persontests positive, then the person should be able to return to normal activity since they would haveimmunity (though whether an infected person develops immunity seems to be currently unknown).One particular test has a “specificity” of 95.6%, which means that the probability of a false positiveis 4.4%. The test has a “sensitivity” of 93.8%, which means that the probability of a false negativeis 6.2%. These numbers look impressive, and the numbers for this test are much better than most.However, notice that a false positive rate of around 4.4% is substantial compared to the proportionof people infected (1% to 5%).(1) Suppose that 5% of the people have been infected. Given that the test comes back positive fora randomly selected person, what is the probability that that person has been infected withCovid-19?(2) Suppose that 1% of the people have been infected. Given that the test comes back positive fora randomly selected person, what is the probability that that person has been infected withCovid-19?(3) Even if we assume that a prior infection bestows immunity, is it reasonable for a person receiv-ing a positive serological test to assume that they have immunity?

Recorded in the table below are the blood pressure measurements (in millimeters) for a sample of 12 adults. Does there appear to be a linear relationship between the diastolic and systolic blood pressures? At the 5% significance level, test the claim that systolic blood pressure and diastolic blood pressure have a linear relationship.

Data Table: Blood Pressure 8

Hypotheses:
H₀: Slope and Correlation are both zero
H₁: Slope and Correlation are both not zero

Results:
What is the correlation coefficient? Use 4 decimal places in answer.
r = _____

What percent of the variation of absences are explained by the model? Round to nearest hundredth percent (i.e. 65.31%).
R²=_____

What is the equation for the regression line? Use 2 decimal places in answers.
Diastolic = (Systolic) + ______

State the p-value. Round answer to nearest hundredth percent (i.e. 2.55%).
p-value = _____

Conclusion:
We_____ sufficient evidence to support the claim that the correlation coefficient and slope of the regression line are both statistically different than zero (p__ 0.05).
(Use “have” or “lack” for the first blank and “<” or “>” for the second blank.)