<< Chapter < Page Chapter >> Page >

What type of data is the number of 20 year olds considered to be?

quantitative - discrete

On average, a busy emergency room gets a patient with a shotgun wound about once per week. We are interested in the number of patients with a shotgun wound the emergency room gets per 28 days.

  • Define the random variable X size 12{X} {} .
  • State the distribution for X size 12{X} {} .
  • Find the probability that the emergency room gets no patients with shotgun wounds in the next 28 days.
  • P 4 size 12{P left (4 right )} {}
  • 0.0183

The next two questions refer to the following information:

The probability that a certain slot machine will pay back money when a quarter is inserted is 0.30 . Assume that each play of the slot machine is independent from each other. A person puts in 15 quarters for 15 plays.

Is the expected number of plays of the slot machine that will pay back money greater than, less than or the same as the median? Explain your answer.

greater than

Is it likely that exactly 8 of the 15 plays would pay back money? Justify your answer numerically.

No; P x = 8 = 0 . 0348 size 12{P left (x=8 right )=0 "." "0348"} {}

A game is played with the following rules:

  • it costs $10 to enter
  • a fair coin is tossed 4 times
  • if you do not get 4 heads or 4 tails, you lose your $10
  • if you get 4 heads or 4 tails, you get back your $10, plus $30 more

Over the long run of playing this game, what are your expected earnings?

You will lose $5

  • The mean grade on a math exam in Rachel’s class was 74, with a standard deviation of 5. Rachel earned an 80.
  • The mean grade on a math exam in Becca’s class was 47, with a standard deviation of 2. Becca earned a 51.
  • The mean grade on a math exam in Matt’s class was 70, with a standard deviation of 8. Matt earned an 83.

Find whose score was the best, compared to his or her own class. Justify your answer numerically.

Becca

The next two questions refer to the following information:

A random sample of 70 compulsive gamblers were asked the number of days they go to casinos per week. The results are given in the following graph:

Histogram of 5 bars with relative frequency on the y-axis, from 0.1-0.3 in increments of 0.1, and number of days on the x-axis, from 0-7 in increments of 1. No bars are present for 4 or 6.

Find the number of responses that were “5".

14

Find the mean, standard deviation, the median, the first quartile, the third quartile and the IQR.

  • Sample mean = 3.2
  • Sample standard deviation = 1.85
  • Median = 3
  • Quartile 1 = 2
  • Quartile 3 = 5
  • IQR = 3

Based upon research at De Anza College, it is believed that about 19% of the student population speaks a language other than English at home.

Suppose that a study was done this year to see if that percent has decreased. Ninety-eight students were randomly surveyed with the following results. Fourteen said that they speak a language other than English at home.

  • State an appropriate null hypothesis.
  • State an appropriate alternate hypothesis.
  • Define the Random Variable, p ̂ size 12{P'} {} .
  • Calculate the test statistic.
  • Calculate the p-value.
  • At the 5% level of decision, what is your decision about the null hypothesis?
  • What is the Type I error?
  • What is the Type II error?
  • z = 1 . 19 size 12{z= - 1 "." "19"} {}
  • 0.1171
  • Do not reject the null

Assume that you are an emergency paramedic called in to rescue victims of an accident. You need to help a patient who is bleeding profusely. The patient is also considered to be a high risk for contracting AIDS. Assume that the null hypothesis is that the patient does not have the HIV virus. What is a Type I error?

We conclude that the patient does have the HIV virus when, in fact, the patient does not.

It is often said that Californians are more casual than the rest of Americans. Suppose that a survey was done to see if the proportion of Californian professionals that wear jeans to work is greater than the proportion of non-Californian professionals. Fifty of each was surveyed with the following results. 15 Californians wear jeans to work and 6 non-Californians wear jeans to work.

  • C size 12{C} {} = Californian professional
  • NC size 12{ ital "NC"} {} = non-Californian professional
  • State appropriate null and alternate hypotheses.
  • Define the Random Variable.
  • Calculate the test statistic and p-value.
  • At the 5% significance level, what is your decision?
  • What is the Type I error?
  • What is the Type II error?
  • z = 2.21 size 12{z=1 "." "73"} {} ; p = 0.0136 size 12{p=0 "." "0419"} {}
  • Reject the null
  • We conclude that the proportion of Californian professionals that wear jeans to work is greater than the proportion of non-Californian professionals when, in fact, it is not greater.
  • We cannot conclude that the proportion of Californian professionals that wear jeans to work is greater than the proportion of non-Californian professionals when, in fact, it is greater.

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Collaborative statistics using spreadsheets. OpenStax CNX. Jan 05, 2016 Download for free at http://legacy.cnx.org/content/col11521/1.23
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Collaborative statistics using spreadsheets' conversation and receive update notifications?

Ask