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Q1: The scale skilled, semi-skilled, and unskilled laborer was used to classify respondents in a recent survey. The appropriate measure(s) of central tendency for this variable are

a. the mode.

b. the median.

c. the mode and the median.

d. the mean.

e. the mode, the median, and the mean.

Answer: c

Q2: Which of the following statements is FALSE? The t‑test to test an hypothesis about a single population mean

a. assumes the variable is normally distributed

b. applies when the variance of the variable is known

c. applies when the sample size is small; e.g., less than 30

d. is referred to a t‑distribution which is completely determined by its degrees of freedom

e. theoretically applies when the sample is large, e.g., greater than 30, if the general conditions surrounding its use are satisfied

Answer: b

Q3: Weight of a particular component in a box of chemical solution is important in its effectiveness. There are two different brands of this solution available in the market: brand 1 and brand 2. A sample of 10 boxes of brand 1 solution are randomly selected. Average weight of the component measured in this sample is 90.0 mg, with a sample standard deviation of 5.0 mg. A sample of 15 boxes of brand 2 solution are randomly selected and sample mean and standard deviation are 87.0 mg and 4.0 mg. The analyst believes the variance of the weight of components in two solution brands are the same. Perform the appropriate hypothesis test for equality of the average of components weights of two brands. Use significance level of 5%.

Answer:

Population variances are not known but equal.

Hypothesis:

Pooled variance:

Test statistics:

Since => Do not reject null hypothesis

With 95% probability, we are confident that there is not enough statistical evidence indicating there is a difference between average weight of the component in two brands of the chemical solution.

Q4: Table below shows the age of a sample of 10 participants in a marketing study and their annual budget for vitamin:

Age

Budget ($)

23

60

45

300

15

40

55

320

18

70

19

80

32

120

35

180

37

150

25

110

Fit a simple linear regression model to this data to predict vitamin budget using age.

Using the model, predict the vitamin budget for a person with age 26.5.

Answer:

(a)

Coefficients

Intercept

-77.861

Age

7.265164

Vitamin budget = -77.861 + 7.265264 * age

(b)

predicted vitamin budget ($) = -77.861 + 7.265264 * 26.5 =114.66

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