a. An experiment was performed on a certain metal to determine if the strength is a function of heating time (hours). Results based on 25 metal sheets are given below. Use the simple linear regression model.
∑X = 50
∑X² = 200
∑Y = 75
∑Y² = 1600
∑XY = 400

Find the estimated y intercept and slope. Write the equation of the least squares regression line and explain the coefficients. Estimate Y when X is equal to 4 hours. Also determine the standard error, the Mean Square Error, the coefficient of determination and the coefficient of correlation. Check the relation between correlation coefficient and Coefficient of Determination. Test the significance of the slope.

b. Consumer Reports provided extensive testing and ratings for more than 100 HDTVs. An overall score, based primarily on picture quality, was developed for each model. In general, a higher overall score indicates better performance. The following (hypothetical) data show the price and overall score for the ten 42-inch plasma televisions (Consumer Report data slightly changed here):

Use the above data to develop and estimated regression equation. Compute Coefficient of Determination and correlation coefficient and show their relation. Interpret the explanatory power of the model. Estimate the overall score for a 42-inch plasma television with a price of $3600 and perform significance test for the slope.

(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)

The population of Nevada, P(t), in millions of people, is a function of t, the number of years since 2010. Explain the meaning of the statement P(8) = 3. Use units and everyday language. (1 point)
2. Find the slope-intercept form of the equation of the line through the points (8, 25) and (-2, -13). (2 points)
3. At 8am, Charles leaves his house in Spartanburg, SC and drives at an average speed of 65 miles per hour toward Orlando, FL. At 11:45am, he stops for lunch in Savannah, GA, which is 276.25 miles from Orlando. a. Find a linear formula that represents Charles’ distance, D, in miles from Orlando as a function of t, time in hours since 8am. (2 points)
b. Find and interpret the horizontal intercept. Remember to write your intercept as a point! (2 points)
c. Find and interpret the vertical intercept. Remember to write your intercept as a point! (2 points)
1
2
4. The temperature in ◦F of freshly prepared soup is given by T(t) = 72 + 118e−0.018t, where t represents time in minutes since 6pm when the soup was removed from the stove. a. Determine the value of T(30) and interpret your answer in everyday language. (2 points)
b. Find and interpret the vertical intercept. Remember to write your intercept as a point! (2 points)
5. Decide whether the following function is linear. Explain how you know without finding the equation of the line.
x 9 12 16 23 34 f(x) 26.6 36.2 49 74.9 110.1
6. Attendance at a local fair can be modeled by A(t) = −30t2 + 309t + 20 people, where t represents the number of hours since 10am. a. Find the average rate of change of the attendance from t = 3 to t = 8. Give units. (2 points)
b. Interpret your answer from (a) in everyday language.

NO HANDWRITTEN ANSWERS PLEASE

The most common abuse of correlation in studies is to confuse the concepts of correlation with those of causation.

Good SAT scores do not cause good college grades, for example. Rather, there are other variables, such as good study habits and motivation, that contribute to both. Find an example of an article that confuses correlation and causation.

Discuss other variables that could contribute to the relationship between the variables.

Bass - Samples: The bass in Clear Lake have weights that are normally distributed with a mean of 1.9 pounds and a standard deviation of 0.8 pounds.

(a) If you catch 3 random bass from Clear Lake, find the probability that the mean weight is less than 1.0 pound. Round your answer to 4 decimal places.


(b) If you catch 3 random bass from Clear Lake, find the probability that the mean weight it is more than 3 pounds. Round your answer to 4 decimal places.

Why are sampling distributions important to the study of inferential statistics? In your answer, demonstrate your understanding by providing an example of a sampling distribution from an area such as business, sports, medicine, social science, or another area with which you are familiar. Remember to cite your resources and use your own words in your explanation.

1) A manufacturer of cereal claims that the mean weight of a particular type of box of cereal is 1.2 pounds. A random sample of 71 boxes reveals a sample average of 1.186 pounds and a sample standard deviation of .117 pound. Using the .01 level of significance, is there evidence that the average weight of the boxes is different from 1.2 pounds?

Is the test statistic for this test Z or t?

Select one:

a. t

b. z

2) A manufacturer of cereal claims that the mean weight of a particular type of box of cereal is 1.2 pounds. A random sample of 71 boxes reveals a sample average of 1.186 pounds and a sample standard deviation of .117 pound. Using the .01 level of significance, is there evidence that the average weight of the boxes is different from 1.2 pounds?

What is the value of the test statistic of the test? ( Enter 0 if this value cannot be determined with the given information.)

3) A manufacturer of cereal claims that the mean weight of a particular type of box of cereal is 1.2 pounds. A random sample of 71 boxes reveals a sample average of 1.186 pounds and a sample standard deviation of .117 pound. Using the .01 level of significance, is there evidence that the average weight of the boxes is different from 1.2 pounds?

What is the pvalue of the test? (Enter 0 if this value cannot be determined with the given information.)

4) A manufacturer of cereal claims that the mean weight of a particular type of box of cereal is 1.2 pounds. A random sample of 71 boxes reveals a sample average of 1.186 pounds and a sample standard deviation of .117 pound. Using the .01 level of significance, is there evidence that the average weight of the boxes is different from 1.2 pounds?

What is the relevant bound of the rejection region? (Enter 0 if this value cannot be determined with the given information.)

5) A manufacturer of cereal claims that the mean weight of a particular type of box of cereal is 1.2 pounds. A random sample of 71 boxes reveals a sample average of 1.186 pounds and a sample standard deviation of .117 pound. Using the .01 level of significance, is there evidence that the average weight of the boxes is different from 1.2 pounds?

What decision should be made?

Select one:

a. Do not reject the null hypothesis

b. Can not be determined from given information

c. Accept the null hypothesis

d. Reject the null hypothesis

Norrie sees two lights flash at the same time, then one of them flashes every 4th second, and the other flashes every 5th second. How many times do they flash together during a whole minute?

Twocombinationdrugtherapies(TreatmentAandTreatmentB)have been developed for eradicating Helicobacter pylori in human patients. The effectiveness of these treatments depends on whether or not the patient is resistant to the chemical compound Metronidazole, but apatient’s resistance status is not routinely determined before beginningtreatment. Treatment A successfully eradicates Helicobacter pylori in 92% of resistant patients and 87% of non-resistant patients. The corresponding proportions for Treatment B are 75% and 95%.

(i) Denote by θ (0 < θ < 1) the proportion of the affected population that is resistant. If a patient from this population is unsuccessfully treated with Treatment B, write down an expression for the probability that the patient is resistant.

(ii) For what values of θ would a greater proportion of patients from this population be successfully treated by Treatment B than by Treatment A?

(iii) Suppose that θ = 0.2. If 20 patients, selected at random from the affected population, are independently treated with Treatment B, find the probability that at least 18 of them will be treated successfully.

A survey conducted of 1,000 college students asked those who regularly drink alcohol, how many alcoholic beverages they consume each week. From this survey, on average (mean), these students consume five beverages each week. These data are normally distributed. The mean, median and mode are equal, and the standard deviation is 1.

1. How many of these students consume five or more alcoholic beverages each week?

2. What is the probability that a student in this study will consume five or more alcoholic beverages each week? (decimal)

3. How many of these adolescents consume five or less alcoholic beverages each week?

4. What is the probability that a student in this study will consume five or less alcoholic beverages each week? (decimal)

5. How many of these adolescents consume between four and six alcoholic beverages each week? 6. What is the probability that a student in this study will consume from four to six alcoholic beverages each week? (decimal)

Given their performance record and based on empirical rule what would be the lower bound of the range of sales values that contains 68% of the monthly sales?

The probability of winning in a certain state lottery is said to be about 1/9. If it is exactly 1/9, what a random variable represents the distribution of the number of tickets a person must purchase up to and including the first winning ticket? Plot the PMF of this random variable. the distribution of the number of tickets purchased up to and including the second winning ticket can be described by what distribution?

1. Two streams (Brimer and Standifer creeks) located in the same watershed are similar in size/shape and most habitat conditions (e.g., temperature, dissolved oxygen, channel substrate); however, they exhibit different pH values. Brimer Creek has a mean pH of 6.1, whereas Standifer Creek has a pH of 5.6. A stream ecologist wishes to determine whether the pH has an influence on the local distributions of benthic macroinvertebrates (annelids, crustaceans, insects) in the two streams. Two study sites were established (one in each stream) that are in close proximity to each other (~50 m apart, separated by a ridge) and located near the mouths of their respective streams. Benthic invertebrates were collected at the two sites using a standardized kick-sampling technique (equal sampling times and areas). Invertebrates were counted in samples from the two sites. The data are summarized below. Number of invertebrates per sample: Brimer Creek, n = 1373 individuals Standifer Creek, n = 955 individuals Perform a G-test for goodness of fit (α = 0.05) to test the ecologist’s hypothesis.

Each of the distributions below could be used to model the time spent studying for an exam. Take 1,000 random samples of size 25 from each of the distributions below. In each case (a,b,c), plot the empirical distribution of the sample mean, estimate the mean of the sample mean, and estimate the standard deviation of the sample mean. Compare the results to the theoretical results.

a. N(5, 1.5²)

b. Unif(0,10)

c. Gamma(5,1)

Suppose that cholesterol levels for women in the U.S. have a mean of 188 and a standard deviation of 24. A random sample of 20 women in the U.S. is selected. Assume that the distribution of this data is normally distributed.

Are you more likely to randomly select one woman with a cholesterol level of more than 200 or are you more likely to select a random sample of 20 women with a mean cholesterol level of more than 200? Explain.