Stat Exam 3
The test statistic t= (x ̄- μ)/(s⁄(√n)) measures A) the maximum distance between the observed x̄ and the claimed parameter value μ0. B) how many standard errors the observed x̄ is from the claimed parameter value μ0. C) the variability of the sample x 's about the claimed parameter value μ0. D) the total number of standard deviations, or σ , units x is from the claimed parameter value μ0.
B
67. P-value is the probability that the null hypothesis is true
F
68. When we fail to reject H0, we may have made a type I error.
F
69. A large P-value proves H0 is true
F
70. Power is the probability that Ha is believed when H0 is true.
F
72. If you reject the null hypothesis, you cannot make a type I error.
F
73. α is found in the fail to reject H0 region under the curve of the sampling distribution defined by H0.
F
74. For fixed α, increasing sample size increases β.
F
77. The margin of error for a 90% confidence interval is larger than the margin of error for a 99% confidence interval (all other things being equal.)
F
Type 2 Error
Fail to reject H0 when H0 is false
we can use confidence interval to perform a test of significance if
Ha is 2 sided the confidence level and significance level add up to 100%
Type 1 Error
Reject H0 when H0 is true
64. T/F: The shape of the t-distribution gets closer and closer to the shape of standard Normal distribution as the degrees of freedom increase.
T
66. The mean of every t-distribution is zero just like the standard Normal distribution
T
71. For fixed sample size, increasing α decreases β.
T
75. For fixed α, increasing sample size increases power.
T
76. All statistical inferential procedures require either random sampling or random allocation.
T
78. Increasing the sample size from 100 to 500 decreases the margin of error for a 95% confidence interval.
T
definition of p-value according to online
The P-value is the level of marginal significance within a statistical hypothesis test, representing the probability of the occurrence of a given event. The p-value is used as an alternative to rejection points to provide the smallest level of significance at which the null hypothesis would be rejected.
Proper statement for Confidence Interval
We are 95% confident that mu is within (range) Or we are 95% confident that the interval (range) contains mu
10. Sample results are said to be statistically significant whenever a) the difference between the observed statistic and the claimed parameter value given in H0 is too large to be due to chance. b) the difference between the true situation and the observed situation could plausibly have resulted because H0 is false. c) the researcher subjectively classifies the observed deviation from what was expected under H0 as large enough to matter. d) the difference between the observed statistic and the claimed parameter value is large enough to be worth reporting.
a
40. Which one of the following is NOT part of the definition for P-value? a) Probability that the null hypothesis is true. b) Probability of obtaining a value of the statistic. c) The value of the statistic is farther from the claimed parameter value than the observed statistic. d) The null hypothesis is assumed to be true.
a
51. If we decrease our level of confidence, keeping all else constant, our margin of error will a) decrease. b) increase. c) remain the same. d) change, but we can't predict whether it will increase or decrease.
a
59. Tests of significance on μ and confidence intervals for μ (with σ known) are based on a) the sampling distribution of x̄. b) the shape of the population distribution. c) the Law of Large Numbers. d) the language of sample designs
a
Fill in the blank: The t-distribution with 8 degrees of freedom has ____________________ the standard Normal distribution. a) the same center but is more spread out than b) the same center but is less spread out than c) the same center and spread as d) a different center and a different spread than
a
alpha = Beta = Power =
a = probability of Type 1 error B = probability of Type 2 error Power = probability of rejecting H0 when its false
standard error of p-hat
an estimate of the standard deviation of sampling distribution of p-hat
14. The margin of error in a confidence interval covers only which kind of errors? a) interviewer errors b) errors due to random sampling c) bias errors due to wording of questions d) computational errors
b
22. What two things do we need in order to compute margin of error for a one-sample t confidence interval for μ? a) Sample size and level of confidence. b) Level of confidence and the standard error of x̄. c) Values for μ and σ. d) The mean and standard deviation of the sampling distribution of x̄.
b
28. How is level of confidence determined? a) From the confidence intervals. b) Subjectively determined by the researcher. c) The probability that the observed statistic falls in the confidence interval. d) Computed from margin of error. e) From the sample size: the larger the sample size, the larger the level of confidence.
b
We use a t-distribution with n-1 degrees of freedom rather than the standard normal distribution whenever a) the Central Limit Theorem does not apply. b) we are using s to estimate σ. c) the population is not Normally distributed. d) we can apply the Law of Large numbers and do not need normality.
b
12. When using a confidence interval to perform a two-sided test, H0 will be rejected whenever a) the claimed parameter value in H0 falls inside the confidence interval. b) the observed statistic value from the sample falls inside the confidence interval. c) the claimed parameter value in H0 falls outside the confidence interval. d) the observed statistic value from the sample falls outside the confidence interval.
c
13. Suppose you are testing the following hypotheses. What is the type I error for these hypotheses? H0: Cake is not done versus Ha: Cake is done a) To believe that the cake is not done when it is still not done. b) To believe that the cake is not done when it really is done. c) To believe that the cake is done when it is still not done. d) To believe that the cake is done when it really is done.
c
25. Refer to the above question. Suppose x̄ = 50.15 bushels per acre. Graphically, what represents the P-value? a) The area under the sampling distribution of x̄ curve between 50 and 50.15. b) The area under the sampling distribution of x̄ curve to the left of 50.15. c) The area under the sampling distribution of x̄ curve to the right of 50.15. d) The probability that H0 is true if x̄ = 50.15.
c
42. What do we obtain from the sampling distribution of x̄, created assuming the null hypothesis is true, in order to perform a test of hypothesis? a) Sample size. b) Level of significance or α. c) P-value. d) The value of x̄.
c
46. What is the purpose of a confidence interval? a) to measure the amount of confidence you have in your interval b) to determine the percentage of times the parameter will fall into your interval c) to estimate the value of a parameter d) to give a range of reasonable probability simulations
c
50. Which one of the following is NOT a correct statement about margin of error? a) A small margin of error says that we have pinned down the parameter quite precisely. b) For fixed level of confidence, increasing the sample size, n, reduces the margin of error. c) For fixed sample size, decreasing level of confidence increases the margin of error. d) To obtain a smaller margin of error without increasing sample size, you must be willing to accept lower confidence.
c
53. Level of confidence can be defined as a) the probability that the computed confidence interval contains the value of the parameter b) the percentage of the time the confidence interval will contain the statistic measured. c) the percentage of the time that the confidence interval procedure will give you a confidence interval that contains the parameter value. d) a percentage between 0 and 100 that tells us how often the assumptions for the procedure are met.
c
55. The null hypothesis is a statement of a) the many possible values of the statistic. b) how well the statistic estimates the parameter to be tested. c) no effect or no change in the population parameter. d) an estimate of a population parameter.
c
16. The purpose of a confidence interval is to provide a) information about the range of data in a distribution. b) a measure of the confidence we can have in our sample results representing the population. c) a list of all possible values of the statistic from all possible samples. d) plausible values that a parameter could be.
d
30. Level of confidence can be defined as a) the probability that a computed confidence interval contains the unknown parameter value. b) the percentage of time that the observations or measurements fall in the confidence interval. c) the probability that the observed statistic is in the confidence interval. d) the percentage of the time that the procedure will produce intervals that contains the parameter value.
d
39. Which one of the following does NOT affect margin of error for a one-sample t confidence interval for μ? (Assume that the necessary conditions are met.) a) Level of confidence b) Sample size c) Standard error of x̄ d) Value of the parameter μ.
d
56. What does significant in the statistical sense mean? a) no difference. b) of great importance. c) that the test statistic supports the null hypothesis. d) not likely to happen just by chance if H0 were true.
d
58. All of the following are true statements about the P-value except one. Which statement is false? a) P-value is the area in the tail of the sampling distribution defined by H0. b) The smaller the P-value, the greater the evidence for the alternative hypothesis. c) The larger the P-value, the greater the agreement between the data and H0. d) P-value is used to determine the significance level.
d
35. Suppose we have H0: μ = 30 versus Ha: μ > 30 with P-value = .032. If we decided to test H0: μ = 30 versus Ha: μ ≠ 30, what is the P-value for this new Ha assuming all other factors are the same? a) .016 b) .032 c) .050 d) .064
d b/c just multiply p-value by 2
use t when
data is SRS sigma unknown
increasing sample size will _____ width of confidence interval
decrease
27. Statistically significant is equivalent to all of the following except one. Which one is not equivalent? a) P-value < α. b) The difference between the observed value of the statistic and the value of the parameter as given in H0 is too large to attribute to just chance variation. c) The probability of obtaining a sample statistic as extreme or more extreme than actually observed if H0 were true is too small for us to believe that H0 is correct. d) The observed statistic is inconsistent with the null hypothesis. e) The difference between an observed statistic and the true parameter value is due to chance variation.
e
One Sample z-test for population proportion
find null value H0 : p = p0, n and alpha compute p-hat check conditions (random sample and normal (conditions)) compute test statistic find p-value (put in chart) **If its 2 sided then multiply p-value times 2
Steps of making confidence interval
find p-hat, sample size and level of confidence check conditions (random and normal) compute interval
null hypothesis
initial belief--assume true
conditions for confidence interval
randomness of data collection normality of sampling distribution of x-bar sigma known
smaller df = larger df =
smaller df- larger the spread (more uncertainty) larger df-closer to standard normal
t-distribution used when
standard deviation unknown
standard error of x-bar
the estimate of the standard deviation of the sampling distribution of x̄.
alternative hypothesis
what might think otherwise
