Jeopardy Statistics Edition

Terms Calculator Commands Sampling Distributions Confidence Intervals Hypothesis Tests: Proportions Hypothesis Tests: Means $400 $600 $800 $1000 $200 $400 $600 $800 $1000 $200

Final Jeopardy

CATEGORY: Hypothesis Tests

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: H 0 : p = 0.70 H a : p ≠ 0.70

Final Jeopardy What is a Type II error since we would Fail to Reject H 0 ? Running 1-PropZTest z = P-value =

Terms: $200 A statement about the value of some population parameter that is assumed to be true.

Terms: $200 What is the null hypothesis or H 0 ? ?

Terms: $400 The probability of making a Type I error in a hypothesis test.

Terms: $400 What is the level of significance or  ? ?

Terms: $600 A range of plausible values for a population parameter that is determined from a single random sample.

Terms: $600 What is a confidence interval? ?

Terms: $800 The probability of getting a sample comparable to the one we have under the assumption that the null hypothesis is correct.

Terms: $800 What is the P-value of a hypothesis test? ?

Terms: $1000 The value of some probability variable corresponding to the sample data collected.

Terms: $1000 What is the test statistic for a hypothesis test? ?

Calculator Commands: $200 To construct a confidence interval for the proportion of all XU students that will study for their final exam.

Calculator Commands: $200 What is “1-PropZInt…” ?

Calculator Commands: $400 To calculate a P-value for hypotheses involving a single population proportion.

Calculator Commands: $400 What is “normalcdf” ? ?

Calculator Commands: $600 To conduct a hypothesis test comparing two population means using the P-value approach.

Calculator Commands: $600 What is “2-SampTTest…” ?

Calculator Commands: $800 To construct a confidence interval for the difference in the proportion of females planning to study for finals and the proportion of men planning to study for finals.

Calculator Commands: $800 What is “2-PropZInt…” ?

Calculator Commands: $1000 To compute the P-value comparing the proportion of XU students that have various eye colors (blue, green, brown, hazel).

Calculator Commands: $1000 What is “  2 cdf” ? ?

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 ? ?

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: $400 What is ? ?

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: $800 What is ? ?

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: $1000 What is $ and above? ?

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: $200 What is (156.41mg, mg)? Using Tinterval with “Stats” given ?

Confidence Intervals: $400 This is equal to half the width of a confidence interval.

Confidence Intervals: $400 What is the margin of error of the confidence interval? ?

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: $600 What is 475 subjects? ?

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: $800 What is 96 subjects? ?

Confidence Intervals: $1000 A confidence interval has been constructed from a sample of size 100. If we are to construct another confidence interval with the ME ½ the margin of error of the first, this is the sample size needed.

Confidence Intervals: $1000 What is 400? ?

Hyp. Tests: Proportions: $200 This is the P-value of a two-tailed test that has test statistic z =

Hyp. Tests: Proportions: $200 What is ? ?

Hyp. Tests: Proportions: $400 This is the P-value for a hypothesis test having: H 0 : p 1 = 0.2, p 2 = 0.4, p 3 = 0.3, p 4 = 0.1 Test statistic: X 2 = 10.42

Hyp. Tests: Proportions: $400 What is ? ?

Hyp. Tests: Proportions: $600 This is the validity for a hypothesis test about a single population proportion.

Hyp. Tests: Proportions: $600 What is –(a) A properly obtained, random sample –(b) np ≥ 10 and n(1-p) ≥ 10 ?

Daily Double

Hyp. Tests: Proportions: $800 This is the test statistic obtained (give the calculation and the value) from a sample of size 90 in which there were 62 ”successes” for the hypotheses: H 0 : p = 0.72 H a : p < 0.72

Hyp. Tests: Proportions: $800 What is z = ? ?

Hyp. Tests: Proportions: $1000 This is the 95% CI and conclusion reached for a sample of size 300 having 210 “successes” for the hypotheses: H 0 : p = 0.75 H a : p ≠ 0.75

Hyp. Tests: Proportions: $1000 What is ( , ) and thus we Fail to Reject H 0 ? Using 1-PropZInt and noticing 0.75 is in the interval. ?

Hyp. Tests: Means: $200 This is what we do not know that results in having to use a Gosset t curve rather than the z-curve when performing tests about population means.

Hyp. Tests: Means: $200 What is σ, the population’s standard deviation? ?

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 = for the hypotheses: H 0 : μ = 78 H a : μ ≠ 78

Hyp. Tests: Means: $600 What is ? ?

Hyp. Tests: Means: $800 This is the test statistic and P-value obtained from a sample of size 16 with mean hours and standard deviation hours for the hypotheses: H 0 : μ = 1400 H a : μ > 1400

Hyp. Tests: Means: $800 What is t = 1.57 with P-value = ? ?

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: H 0 : μ f = μ m H a : μ f < μ m

Hyp. Tests: Means: $1000 What is t = , P-value = , and thus we Reject H 0 to conclude that on average, women do make less at this company than men? Using 2-SampTTest ?