# Mathematics

**5) A time series trend equation for Hammer Hardware is Y’ = 5.6 + 1.2t, where sales are in millions of dollars and t increases by one unit for each year. If the value of sales in the base year of 2016 is $5.6 million, what would be the estimated sales amount for 2018?**

$8 million

$6.8 million

Unable to determine from given information

$5.6 million

**6) 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:**

t test for difference in paired samples

z test for two population proportions

z test for two population means

t test for two population means

**7) 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?**

z = -2.45

z = -5.44

z = -1.81

z = – 3.90

**8) 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? **

H1: µ ≠ 6.6

H1: µ ≥ 6.6

H1: µ > 7.6

H1: µ = 6.6

**9) As the size of the sample increases what happens to the shape of the distribution of sample means? **

It approaches a normal distribution.

It cannot be predicted in advance.

It is positively skewed.

It is negatively skewed.

**10) 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? **

You would reject Ho

You would accept Ho

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

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

**11) 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? **

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.

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

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

**12) 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? **

0.3413

0.5000

0.4332

0.1932

**13) The MacBurger restaurant chain claims that the waiting time of customers for service is normally distributed, with a mean of 3 minutes and a standard deviation of 1 minute. The quality-assurance department found in a sample of 50 customers at the Warren Road MacBurger that the mean waiting time was 2.75 minutes. When you perform a test of hypothesis, what would be the resulting p-value? **

.0586

.0384

.0471

.0512

**14) 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? **

1.00

Very likely

0.4332

0.8664

**15) In a distribution, the second quartile corresponds with the __________.**

Variance

Mode

Median

Mean

**16) 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? **

.40

.30

.030

.50

**17) The Director of Golf for a local course wants to study the number of rounds played by members on weekdays. He gathered the sample information shown below for 520 rounds. At the .05 significance level, is there a difference in the number of rounds played by day of the week?**

**Day**

**Rounds**

Monday

124

Tuesday

74

Wednesday

104

Thursday

98

Friday

120

No, because χ2 = 11.793

Yes, because χ2 = 15.308

No, because χ2 = 7.715

Yes, because χ2 = 12.288

**18) Which approach to probability assumes that the events are equally likely?**

Empirical

Mutually exclusive

Classical

Subjective

**19) Sales at a fast-food restaurant average $6000 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 _______. **

1.96

6,000

6,400

2.8

**20) A study by the National Park Service revealed that 50% of the vacationers going to the Rocky Mountain region visit Yellowstone Park, 40% visit the Grand Tetons, and 35% visit both. What is the probability that a vacationer will visit at least one of these magnificent attractions? **

0.35

0.55

0.95

0.05

**21) The ages of all the patients in the isolation ward of the hospital are 38, 26, 13, 41, and 22. What is the population standard deviation? **

6.92

10.33

15.85

9.26

**22) 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? **

13.5 and 14.5 inches

13.9 and 14.1 inches

13.0 and 15.0 inches

13.8 and 14.2 inches

**23) 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?**

z = -1.29

t = -1.25

t = -1.07

z = -1.11

**24) 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? **

1/3 or 0.33

1/13 or 0.077

1/4 or 0.25

12/13 or 0.923

**25) An example of a qualitative variable is _________________. **

Weight of a person

Miles between oil changes

Number of children in a family

Color of ink in a pen

**26) Which of the following is true regarding the normal distribution? **

It has two modes.

The points of the curve meet the x-axis at z = -3 and z = 3.

It is asymmetrical.

The mean, median, and mode are all equal.

**27 )What is the range of values for a coefficient of correlation? **

Unlimited range

0 to +1.0

-1.0 to +1.0 inclusive

-3 to +3 inclusive

**28) Consider the following regression analysis between sales (Y in $1000) and social media advertising (X in dollars). = 55,000 + 7X**

The regression equation implies that an:

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 $62,000 in sales.

increase of $7 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.

**29) When statisticians analyze sample data in order to draw conclusions about the characteristics of a population, this is referred to as: **

Descriptive statistics

Data summarization

Statistical inference

Data analysis

**30) What is the median of 26, 30, 24, 32, 32, 31, 27, and 29? **

32

29.5

30

29