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# Basic Statistics Questions

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** Please see the attached file. **

(1) Find the median of the following set of numbers:
1, 4, 9, 15, 25, 36

(2) Find the mode of the following set of numbers:
41, 43, 56, 67, 69, 72

(3) Find the mode of the following set of numbers:
9, 8, 10, 9, 9, 10, 8

(4) A salesperson drove 238, 159, 87, 163, and 198 miles on a 5-day trip. What was the mean number of miles driver per day?

(5) The following scores were recorded on a 200-point final examination:
193, 185, 163, 186, 192, 135, 158, 174, 188, 172, 168, 183, 195, 165, 183.
a) Find the mean final examination score.
b) Find the median final examination score
c) Is the mean or median a more useful representative of the final examination scores? Write a brief paragraph justifying you response.

(6 - 13) For the problems below, use the following chart:
[see attachment]

What is the population of Europe in 2000?
What is the total area of Europe?
Compare the population per square mile in Asia to the population per square mile in North America for the year 2000.
What is the percent increase in the population for all six inhabited continents, excluding Asia, from 1950 to 2000.,
What was the percent increase in the population in South America from 1900 to 2000?
What was the mean population of the six continents or land masses that were habitable in 2000?
What was the mean population in 1950?
What was the percent increase in the mean population from 1950 to 2000?

(14 - 15) Use the graph below to answer this question. It shows the number of robberies in a town during the last 6 months.
[see attachment]

How many robberies occurred in November?
What was the mean number of robberies per month over the last 6 months?

(16) Use the following graph and table to predict the payment for 2005:
[see attachment]

(17) The table below gives the median earnings of women aged 25 and older who work full time, year round, by educational attainment, according to the 2000 census.
[see attachment]

Create a bar graph using this information. You can use MS Excel or PowerPoint.

(18) The following pie chart shows the budget for a local company. The total budget is \$600,000.
[see attachment]

Find the amount budgeted in the "operating expenses" category.

(19) The following pie chart shows the distribution of a person's total yearly income of \$24,000.
[see attachment]

Find the amount budgeted for the category of Utilities.

(20) The following table gives the number of Senate members with military service in the 106th Congress, by branch.
[see attachment]

Construct a pie chart from this information.

(21) Find the median of the set of the following set of numbers:
26, 30, 38, 67, 59, 21, 17, 85, 22, 22

(22) Give the five number summary of the following set of numbers:
7, 7, 5, 4, 1,9, 8, 8, 8, 5, 2

(23) Find the range of the following set of numbers:
7, 7, 5, 4, 1, 9, 8, 8, 8, 5, 2

#### Solution Preview

Section Problem

8.1 14 Find the median of the following set of numbers.
1, 4, 9, 15, 25, 36
The median is the number in the middle of the list. The median of this set of numbers is the average of the two middle numbers (since there isn't one "middle"). The median is (15 + 9)/2 = 24/2 = 12

8.1 18 Find the mode of the following set of numbers:
41, 43, 56, 67, 69, 72
The mode is the number that occurs the most often in the list. There is no mode in this set of numbers, because every number only

8.1 20 Find the mode of the following set of numbers:
9, 8, 10, 9, 9, 10,
The mode of this list is 9. The number 9 occurs three times, while the other numbers only occur

8.1 24 A salesperson drove 238, 159, 87, 163, and 198 miles on a
5-day trip. What was the mean number of miles driver per day?
The mean is the average. Add the numbers together, then divide by the number of data points you have.
The mean is:
(238 + 159 + 87 + 163 + 198)/5 = 845/5 = 169

8.1 36 The following scores were recorded on a 200-point final examination: 193, 185, 163, 186, 192, 135, 158, 174, 188, 172, 168, 183, 195, 165, 183.
(a) Find the mean final examination score.
The mean is 2638/15 = 175.867.
(b) Find the median final examination ...

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## Explaining 6 Basic Statistics Questions on Hypothesis Testing

I am just wanting someone to see if answered these word questions correctly. My book isn't exactly to the direct point. I understand if your unable to.

Which of the following accurately describes the critical region?
* outcomes with a high probability if the null hypothesis is true
* outcomes with very low probability if the null hypothesis is true (this is the one i selected?)
* outcomes with a high probability whether or not the null hypothesis is true
* outcomes with a very low probability whether or not the null hypothesis is true

with o= .05, how are the boundaries for the critical region determined?
* boundaries are drawn so there is 5% (0.5) in the center of the distribution
* boundaries are drawn so there is 5 % (.05) in each tail (this is what i chose, but i am torn between it and the 2.5% because of each tail?)
* boundaries are drawn so there is 2.5% (.025) in each tail
* boundaries are drawn so there is 10% (.10) in each tail of the distribution

If a hypothesis test produces a z score in the critical region, what decision should me made?
*fail to reject the null hypothesis
* fail to reject the alternative hypothesis
* reject the alternative hypothesis
* reject the null hypothesis (this is the one i had chosen?)

A sample of n= 25 individuals is selected from a population with u=80 and a treatment is administered to the sample. what is expected if the treatment has no effect?
* the sample mean should be very different from 80 and should lead you to fail to reject the null hypothesis
* the sample mean should be close to 80 and should lead you to fail to reject the null hypothesis
* the sample mean should be very different from 80 and should lead you to reject the null hypothesis
* the sample mean should be close to 80 and should lead you to reject the null hypothesis. ( this is the one that i had chosen?)

which of the following is an accurate definition of a type 1 error?
* rejecting a false null hypothesis
* rejecting a true null hypothesis (this is the one i had chosen?)
* failing to reject a false null hypothesis
* failing to reject a true null hypothesis

which of the following is an accurate definition of a type II error?
* rejecting a true null hypothesis
* rejecting a false null hypothesis
* failing to reject a true null hypothesis
* failing to reject a false null hypothesis ( this is the one i had chosen?)

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