# Mathematics

1. You perform a hypothesis test at the .05 level of significance. Your computed p-value turns out to .042. What is your decision about the hypothesis?

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You would accept Ho if it is a two-tailed test, but reject Ho if a one-tailed test

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You would reject Ho

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You can’t render a decision unless you know the computed test statistic

You would accept Ho

2. A weight-loss company wants to statistically prove that its methods work. They randomly selected 10 clients who had been on the weight loss program for between 55 and 65 days. They looked at their beginning weights and their current weight. The statistical test they should utilize is:

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t test for two population means

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t test for difference in paired samples

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z test for two population proportions

z test for two population means

3.

Consider the following regression analysis between sales (Y in $1,000) and social media advertising (X in dollars).

= 55,000 + 7X

The regression equation implies that an:

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increase of $7 in advertising is associated with an increase of $7,000 in sales.

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increase of $1 in advertising is associated with an increase of $62,000 in sales.

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increase of $1 in advertising is associated with an increase of $7,000 in sales.

increase of $1 in advertising is associated with an increase of $7 in sales.

9. A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. What is the alternate hypothesis?

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H1: µ > 7.6

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H1: µ = 6.6

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H1: µ ≠ 6.6

H1: µ ≥ 6.6

13. Each month the National Association of Purchasing Managers publishes the NAPM index. One of the questions asked on the survey to purchasing agents is: Do you think that the economy is expanding? Last month, of the 300 responses, 160 answered “yes” to the question. This month, 170 of the 290 responses indicated that the economy is expanding. If you’re testing to find if a larger proportion of agents believe that the economy is expanding this month, what is your computed test statistic?

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z = -1.11

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t = -1.25

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t = -1.07

z = -1.29

14. A coffee manufacturer is interested in whether the mean daily consumption of regular-coffee drinkers is less than that of decaffeinated-coffee drinkers. A random sample of 50 regular-coffee drinkers showed a mean of 4.35 cups per day, with a standard deviation of 1.2 cups per day. A sample of 40 decaffeinated coffee drinkers showed a mean of 5.84 cups per day, with a standard deviation of 1.36 cups per day. What is your computed z-statistic?

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z = -1.81

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z = – 3.90

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z = -5.44

z = -2.45

15. A research firm conducted a survey to determine the mean amount steady smokers spend on cigarettes during a week. A sample of 64 smokers revealed that = $20 and S = $5. What is the 95% confidence interval for μ?

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18.37 to 21.63

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$18.78 to $21.23

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18.16 to 21.84

$18.60 to $21.40

16. The first card selected from a standard 52-card deck was a king. If it is returned to the deck, what is the probability that a king will be drawn on the second selection?

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1/4 or 0.25

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1/3 or 0.33

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1/13 or 0.077

12/13 or 0.923

17. A group of 100 students was surveyed about their interest in a new International Studies program. Interest was measured in terms of high, medium, or low. In the study, 30 students responded high interest, 40 students responded medium interest, and 30 students responded low interest. What is the relative frequency of students with high interest?

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.50

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.40

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.30

.030

18. The tread life of tires mounted on light-duty trucks follows the normal probability distribution with a mean of 60,000 miles and a standard deviation of 4,000 miles. Suppose you bought a set of four tires, what is the likelihood the mean tire life of these four tires is between 57,000 and 63,000 miles?

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1.00

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Very likely

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0.4332

0.8664

19. 19

Sales at a fast-food restaurant average $6,000 per day. The restaurant decided to introduce an advertising campaign to increase daily sales. To determine the effectiveness of the advertising campaign, a sample of 49 days of sales was taken. It found that the average daily sales were $6,400 per day. From past history, the restaurant knew that its population standard deviation is about $1,000. The value of the test statistic is _______.

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6,400

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2.8

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1.96

6,000

20

The distribution of a sample of the outside diameters of PVC pipes approximates a symmetrical, bell-shaped distribution. The arithmetic mean is 14.0 inches, and the standard deviation is 0.1 inches. About 68% of the outside diameters lie between what two amounts?

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13.9 and 14.1 inches

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13.8 and 14.2 inches

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13.0 and 15.0 inches

13.5 and 14.5 inches

University officials say that at least 70% of the voting student population supports a fee increase. If the 95% confidence interval estimating the proportion of students supporting the fee increase is [0.75, 0.85], what conclusion can be drawn?

The interval estimate is above 70%, so infer that it will be supported.

Since this was not based on the population, no conclusion can be drawn.

Seventy percent is not in the interval, so assume it will not be supported.

Seventy percent is not in the interval, so another sample is needed.

The interval estimate is above 70%, so infer that it will be supported.

The mean of a normal distribution is 400 pounds. The standard deviation is 10 pounds. What is the probability of a weight between 415 pounds and the mean of 400 pounds?

The answer for this first one is 0.4332.