Problem 1

Let , , and be independent events where , and are all positive. Then .

• [x] TRUE
• [ ] FALSE

Problem 2

You toss a fair coin and roll a fair die. The chance of tossing a head or rolling a "6" is .

• [ ] TRUE
• [x] FALSE

Problem 3

Let and be independent random variables. Then .

• [ ] TRUE
• [x] FALSE

Problem 4

Let 's be independent random variables each with mean and variance , and define to be the random variable for the sample average of 's. Then has a larger variability than .

• [ ] TRUE
• [x] FALSE

Problem 5

In hypothesis testing, the p-value is the probability that the null hypothesis is true.

• [ ] TRUE
• [x] FALSE

Problem 6

You carry out a hypothesis test at the 5% significance level. Suppose the data provides sufficient evidence to reject the null hypothesis. If the significance level were 10% instead of 5%, the null hypothesis will still be rejected.

• [x] TRUE
• [ ] FALSE

Problem 7

A linear regression line is fitted to some data. One of the data points has a negative residual. This implies the data point falls below the regression line.

• [x] TRUE
• [ ] FALSE

Problem 8

Consider two independent random variables and . and has the following density function:

(a). Find and

(b). Find and

Problem 9

At a police spot check, 10% of cars stopped have defective headlights and a faulty muffler. 15% have defective headlights and a muffler which is satisfactory. If a car which is stopped has defective headlights, what is the probability that the muffler is also faulty?

Problem 10

A local car tire manufacturer guarantees the tires at 48,000 km such that only 2% of its tires will be replaced due to failure before the guaranteed number of kilometres.

(a). What is the Probability that the First Tire that Fails before the Guaranteed Distance is the 50th Tire Sold? Assume that the Tires Are Independent

(b). One Hundred Tires Are Newly Produced. Assuming that the Tires Are Independent, Use an Approximation Method to Approximate the Probability that less than 2 of the New Tires Will Fail before the Guaranteed Distance

Problem 11

The paint used to make lines on roads must reflect enough light to be clearly visible at night. An old type of paint has a mean reflectometer reading of 20. A new type of paint will be considered if its true mean reflectometer reading exceeds 20. A hypothesis test at the 10% significance level will be based on a random sample of size 25, which gives a sample mean reading of 22 and a sample standard deviation of 4. Should the new type of paint be considered?

(a). Which of the following Sets of Hypotheses Should Be Tested?

• [ ] vs.
• [ ] vs.
• [x] vs.
• [ ] vs.

(b). The Test-statistic is

• [x] 2.5
• [ ] 0.5
• [ ] -2.5
• [ ] -0.5

(c). Do You Reject the Null Hypothesis?

• [x] Yes
• [ ] No

Explain: The test statistic falls within the rejection region of as .

(d). Draw Conclusion in the Context of the Question

We can consider the new paint instead of the old paint as it's mean reflection is above the required mean of given a confidence of

Problem 12

An experiment to determine the effect of several methods of preparation for use in commercial yogurt was conducted by a food science research group. Four batches of yogurt were prepared using each of the three methods: traditional, ultra filtration and reverse osmosis. A trained expert then tasted each of the 12 batches, and judged them on a scale from 1 to 10 (1 indicates the best quality, 10 the worst). Assume constant variance and normality of the quality scores for the different preparation methods.

(a). Complete the Anova Table below

Source of Variation	df	Sum of Squares	Mean Squares	F-ratio
Treatment	2	17.30	8.65
Error	9	6.75	0.75
Total	11	24.05		11.53

(b). Do the Data Suggest that the Mean Quality Scores Are Different among the Three Methods of Preparation? Test the Null Hypothesis that the Population Mean Scores Are All Equal at the 5% Significance Level. You Need not Perform Multiple Comparisons regardless of the Results You Obtain

Our F-ratio calculated is much greater than 4.26 so we reject and conclude that the means are significantly different among the 3 methods of preparation.

(c). Give an Estimate for the Common variance of the Quality Scores for the Different Preparation Methods

Problem 13

The monthly rents for studio apartments in downtown Vancouver have a mean of $750 and a standard deviation of $56. Find the probability that the sample average monthly rent of 64 randomly chosen apartments will be between $729 and $764.

Problem 14

A study was conducted to investigate whether the brain size is an indicator of mental capacity. The study researcher drew a random sample of 30 students, and used magnetic resonance imaging (MRI) to determine the brain size of the students. The total pixel count () from a fixed number of MRI scans served as an index for brain size (a larger count indicates a larger brain size). The students' IQ scores and gender information were also collected.

The following shows the scatterplot of IQ () versus MRI pixel count () for the 30 students.

(a). Check the Most Appropriate Answer for the Value of the Correlation Coefficient

• [ ] -0.48
• [ ] -0.03
• [x] 0.68
• [ ] 0.89

(b). The Least Squares Regression line that Predicts Iq from Mri Pixel Count Was Found to Be . it is also given That: , , Residual Sum of Squares (RSS) =

(i). Construct a 90% Confidence Interval for the Population Slope

(ii). Is Brain Size (measured by Mri Pixel count) Useful for Predicting Iq? Test the Appropriate Hypotheses on the Population Slope at

We reject and conclude that brain size is useful for predicting IQ.

(c) The Researcher also Wanted to Compare the Brain Size between the Two Genders. the Mri Pixel Count Data Are Summarized in the below Table. is there Any Evidence that the Mean Brain Size is Different between Male and Female Students? Test the Appropriate Hypotheses at . State Any assumption(s) that You Make to Validate the Test

gender	number of students	sample mean	sample SD
male	13	92.2	7.4
female	17	89.3	5.8

Since 1.20 is smaller than 2.048 we fail to reject and conclude that there is no difference between the brain sizes of males and females.