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Jeopardy. Statistics Edition. $200. $200. $200. $200. $200. $200. $400. $400. $400. $400. $400. $400. $600. $600. $600. $600. $600. $600. $800. $800. $800. $800. $800. $800. $1000. $1000. $1000. $1000. $1000. $1000. Final Jeopardy. CATEGORY: Hypothesis Tests.

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jeopardy
Jeopardy

Statistics Edition

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final jeopardy1
Final Jeopardy

A sample of 80 is collected in which there are 62 successes.

This is the type of error we risk making when testing the hypotheses:

H0: p = 0.70

Ha: p ≠ 0.70

final jeopardy2
Final Jeopardy

What is a Type II error since we would Fail to Reject H0?

Running 1-PropZTest

z = 1.464

P-value = 0.1432

terms 200
Terms: $200
  • The number of outcomes in event E divided by the total number of possible outcomes.
terms 2001

?

Terms: $200
  • What is P(E) or the probability of event E?
terms 400
Terms: $400
  • Two events that cannot occur simultaneously.
terms 4001

?

Terms: $400
  • What are disjoint or mutually exclusive events?
terms 600
Terms: $600
  • Whether or not one event occurs has no bearing on whether or not another event occurs.
  • P(E|F) = P(E)
terms 6001

?

Terms: $600
  • What are independent events?
terms 800
Terms: $800
  • The probability of getting a sample comparable to the one we have under the assumption that the null hypothesis is correct.
terms 8001

?

Terms: $800
  • What is the P-value of a hypothesis test?
terms 1000
Terms: $1000
  • The value of some probability variable corresponding to the sample data collected.
terms 10001

?

Terms: $1000
  • What is the test statistic for a hypothesis test?
general probability 200
General Probability: $200
  • There are 20 marbles in a bag, 5 each of colors red, white, blue, and green. Each color is numbered 1 through 5.
  • One marble is selected. This is the probability that it is blue.
general probability 2001

?

General Probability: $200
  • What is 5/20 = 0.25?
general probability 400
General Probability: $400
  • There are 20 marbles in a bag, 5 each of colors red, white, blue, and green. Each color is numbered 1 through 5.
  • One is selected at random. This is the probability that it is red or has the number 2 or 5 on it.
general probability 4001

?

General Probability: $400
  • What is 11/20 = 0.55?
general probability 600
General Probability: $600
  • There are 20 marbles in a bag, 5 each of colors red, white, blue, and green. Each color is numbered 1 through 5.
  • Three are selected at random without replacement. This is the probability that at least one of the marbles is blue.
general probability 6001

?

General Probability: $600
  • What is 1 – (15/20)*(14/19)*(13/18) = 0.6009?
general probability 800
General Probability: $800
  • A check of dorm rooms on a certain college campus revealed that 38% had refrigerators (R), 54% had TVs (T), and 21% had both.
  • This is the value and meaning of P(T|RC).
general probability 8001

?

General Probability: $800
  • What is the probability that the room has a TV given that it does not have a refrigerator?

0.33/(0.33 + 0.29) = 0.5323?

general probability 1000
General Probability: $1000
  • A recent Maryland highway safety study found that in 77% of all accidents, the driver was wearing a seatbelt (S). Of those wearing a seatbelt, 92% escaped serious injury (I) but only 63% of those not wearing a seatbelt escaped serious injury. One driver is randomly selected.
  • This is the meaning and value of P(SC|IC)
general probability 10001

?

General Probability: $1000
  • What is the probability that the driver was not wearing a seatbelt given that (s)he did not escape serious injury?
sampling distributions 200
Sampling Distributions: $200
  • At a certain company, it is believed that 84% of the employees approve the new benefits package that is being considered. A random sample of 68 employees is selected.
  • These are the center, shape, and spread of the distribution of the sample proportion that approve the benefits package.
sampling distributions 2001

?

Sampling Distributions: $200
  • What is a normal distribution with mean 0.84 and standard deviation 0.0445?
sampling distributions 400
Sampling Distributions: $400
  • At a certain company, it is believed that 84% of the employees approve the new benefits package that is being considered. A random sample of 68 employees is selected.
  • This is the probability that less than 80% of the sample approve of the new benefits package.
sampling distributions 600
Sampling Distributions: $600
  • At a certain company, the average salary is $54000 with a standard deviation of $7800. A sample of 36 employees is chosen at random from this company.
  • These are the center, shape, and spread of the distribution of the sample mean for such samples.
sampling distributions 6001

?

Sampling Distributions: $600
  • What is a normal distribution with mean $54000 and standard deviation $1300?
sampling distributions 800
Sampling Distributions: $800
  • At a certain company, the average salary is $54000 with a standard deviation of $7800. A sample of 36 employees is chosen at random from this company.
  • This is the probability that the average salary of this sample is more than $58000.
sampling distributions 1000
Sampling Distributions: $1000
  • At a certain company, the average salary is $54000 with a standard deviation of $7800. A sample of 36 employees is chosen at random from this company.
  • These average salaries make up the highest 0.5% of all such average salaries.
sampling distributions 10001

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Sampling Distributions: $1000
  • What is $57348.58 and above?
confidence intervals 200
Confidence Intervals: $200
  • This is the 97.4% CI for a population mean constructed from a sample of size 15 with mean 174.6mg and standard deviation 28.3mg if we assume the population is normally distributed.
confidence intervals 2001

?

Confidence Intervals: $200
  • What is (156.41mg, 192.79mg)?
  • Using Tinterval with “Stats” given
confidence intervals 400
Confidence Intervals: $400

• This is equal to half the width of a

confidence interval.

confidence intervals 4001

?

Confidence Intervals: $400
  • What is the margin of error of the confidence interval?
confidence intervals 600
Confidence Intervals: $600
  • This is the minimum sample size that should be used if we want to construct a 95% CI for a population proportion with a margin of error of no more than 4.5 percentage points.
confidence intervals 6001

?

Confidence Intervals: $600
  • What is 475 subjects?
confidence intervals 800
Confidence Intervals: $800
  • This is the minimum sample size that should be obtained if we want to construct a 90% CI for a population mean with margin of error no more than 7.2 when previous studies support that s = 42.8.
confidence intervals 8001

?

Confidence Intervals: $800
  • What is 96 subjects?
confidence intervals 1000
Confidence Intervals: $1000
  • This is what happens to a CI if we keep the confidence level the same but we increase the sample size.
confidence intervals 10001

?

Confidence Intervals: $1000
  • What is the margin of error decreases resulting in a more narrow confidence interval?
hyp tests proportions 200
Hyp. Tests: Proportions: $200
  • This is the P-value of a two-tailed test that has test statistic z = -2.45.
hyp tests proportions 400
Hyp. Tests: Proportions: $400
  • This is the P-value for a hypothesis test having:

H0: p1 = 0.2, p2 = 0.4, p3 = 0.3, p4 = 0.1

Test statistic: X 2 = 10.42

hyp tests proportions 600
Hyp. Tests: Proportions: $600
  • This is the “command” used in the calculator to, using the P-value approach, test the hypotheses :

H0: p1 = p2

Ha: p1 < p2

hyp tests proportions 6001

?

Hyp. Tests: Proportions: $600
  • What is 2-PropZTest?
hyp tests proportions 800
Hyp. Tests: Proportions: $800
  • This is the test statistic obtained from a sample of size 90 in which there were 62 ”successes” for the hypotheses:

H0: p = 0.72

Ha: p < 0.72

hyp tests proportions 8001

?

Hyp. Tests: Proportions: $800
  • What is z = -0.6573?
hyp tests proportions 1000
Hyp. Tests: Proportions: $1000
  • This is the 95% CI and conclusion reached for a sample of size 300 having 210 “successes” for the hypotheses:

H0: p = 0.75

Ha: p ≠ 0.75

hyp tests proportions 10001

?

Hyp. Tests: Proportions: $1000
  • What is (0.64814, 0.75186) and thus we Fail to Reject H0?

Using 1-PropZInt and noticing 0.75 is in the interval.

hyp tests means 200
Hyp. Tests: Means: $200
  • This is what we must know in order to use the z statistic (rather than t) for a hypothesis test about a single population mean.
hyp tests means 2001

?

Hyp. Tests: Means: $200
  • What is σ, the population’s standard deviation?
hyp tests means 400
Hyp. Tests: Means: $400
  • This is the validity needed when performing a ZTest.
hyp tests means 4001

?

Hyp. Tests: Means: $400
  • What is one of:

(i) normal population

(ii) large sample size (C.L.T.)

(iii) a fairly linear normal plot

hyp tests means 600
Hyp. Tests: Means: $600
  • This is the P-value for a sample of size 10 from a normal population that produced test statistic t = -1.34 for the hypotheses:

H0: μ = 78

Ha: μ ≠ 78

hyp tests means 800
Hyp. Tests: Means: $800
  • This is the test statistic and P-value obtained from a sample of size 16 with mean 1472.4 hours and standard deviation 184.6 hours for the hypotheses:

H0: μ = 1400

Ha: μ > 1400

hyp tests means 8001

?

Hyp. Tests: Means: $800
  • What is t = 1.57 with P-value = 0.0686?
hyp tests means 1000
Hyp. Tests: Means: $1000
  • One employee at a certain company believes that women in the company are earning, on average, less than men. A random sample of men and women are selected from this company. For the 175 women, the average salary was $41250 with a standard deviation of $2100. For the 200 men in the sample the average salary was $42000 with a standard deviation of $2400. These are the test statistic, P-value, and conclusion for the hypotheses:

H0: μf = μm

Ha: μf < μm

hyp tests means 10001

?

Hyp. Tests: Means: $1000
  • What is t = -3.227, P-value = 0.00068, and thus we Reject H0 to conclude that on average, women do make less at this company than men?

Using 2-SampTTest