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Jeopardy

Statistics Edition

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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 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

- The number of outcomes in event E divided by the total number of possible outcomes.

Terms: $400

- Two events that cannot occur simultaneously.

Terms: $600

- Whether or not one event occurs has no bearing on whether or not another event occurs.
- P(E|F) = P(E)

Terms: $800

- The probability of getting a sample comparable to the one we have under the assumption that the null hypothesis is correct.

Terms: $1000

- The value of some probability variable corresponding to the sample data collected.

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: $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: $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: $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: $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

- 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: $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

- 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: $200

- What is a normal distribution with mean 0.84 and standard deviation 0.0445?

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

- 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: $600

- What is a normal distribution with mean $54000 and standard deviation $1300?

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

- 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.

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: $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: $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: $1000

- This is what happens to a CI if we keep the confidence level the same but we increase the sample size.

Confidence Intervals: $1000

- What is the margin of error decreases resulting in a more narrow confidence interval?

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

- 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

- 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: $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: $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: $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

- 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: $400

- This is the validity needed when performing a ZTest.

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

- 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

- 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: $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: $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

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