Sampling Distributions
What is the name of the law that states a sample is normally distributed if n>30?
Central Limit Thereom
What two methods can you use to perform a hypothesis test?
1. P-value method
2. Critical value method.
Can you perform a hypothesis test using Minitab?
Yes
In order to use the z-method for finding a confidence interval, the (population/sample) standard deviation has to be (unknown/ known).
Population; Known
T or Z?
A random sample of 35 Hollywood movies made since the year 2010 had a mean length of 121.6 minutes, with a standard deviation of 20.4 minutes.
t-method
Besides the Central Limit Thereom, what is another way to tell if a sample is normally distributed?
If the sample comes from a population that is normally distributed, the sample will exhibit a normal distribution as well.
What are the symbols for the null hypothesis and alternate hypothesis? How do you write them?
Null Hypothesis: H0; μ =
Alternate Hypothesis: H1; μ <, >, ≠
If you are performing a right-tailed test, when computing the critical value in minitab, what should you enter as your input constant?
Give in terms of α.
1-α.
The margin of error is obtained by multiplying what two numbers?
Critical value and the standard error.
If the P-value is greater than the significance level, we should (reject/fail to reject) the null hypothesis.
Fail to reject the null hypothesis.
If the Central Limit Thereom applies, or if the population is normally distributed, how would you find the mean and standard deviation of the sample?
The mean of the sample is equal to the mean of the population.
The standard deviation of the sample is equal to the population standard deviation divided by the square root of the sample size.
A test of H0; μ = 0 versus H1; μ ≠ 0 is performed using a significance level of α=.05. The P-value is .15. Is H0 rejected?
No
What is the difference between calculating p-value/ critical value for Z and T methods.
**More than 1 correct answer.
For T distributions, you have to enter the degrees of freedom.
Also, you cannot use the probability distribution plot for a t-distribution (Because it is not assumed to be normal).
What will happen to the confidence interval if confidence level is increased?
The confidence interval will be come wider.
What is the appropriate way to interpret a confidence interval with a 95% confidence level?
95% of the time, the population mean will fall between the calculated confidence interval.
The National Health and Nutrition Examination Survey reported that in a recent year, the mean serum cholesterol level for U.S. adults was 202, with a standard deviation of 41.A simple random sample of 110 adults is chosen.
Can we assume that the sample is normally distributed, if so find the standard deviation and mean of the sample.
Mean: 202
Standard Deviation: 3.91
Explain a Type 1 and Type 2 error in terms of H0 and the decision to reject/fail to reject.
A type 2 error is when the H0 is false and we fail to reject it.
A type 1 error is when the H0 is true and we reject it.
If Minitab outputs the P-value of a two-tailed t-test as .04, what is the actual measurement of the P-value?
.08
True or False?
If a 95% confidence interval for a population mean is is 1.7< μ< 2.3, then the probability is .95 that the mean is between 1.7 and 2.3.
False
If we decrease the value of the significance level α, we (increase/decrease) the probability of a Type 2 error.
Increase
A sample of size 126 will be drawn from a population will be drawn from a population with a mean 26 and standard deviation 3.
a. Find the probability that x will be between 25 and 27.
b. Find the 55th percentile.
a. .9998
b. 26.03
A random sample of 60 second-graders in a certain school district are give a standardized mathematics skills test. The sample mean score iks 52. Assume the standard deviation of test scores is 15. The nationwide average score on this test is 50. The school superintendent wants to know whether the second gradersin her school district have greater math skills than the nationwide average.
Is H0 rejected at the a=.01 significance level? Be sure to state the P-value.
No H0 is not rejected at the .01 significance level.
P-value = .15
Give the complete directions for performing a hypothesis tests in Minitab (t).
Will be demonstrated in Minitab.
In a sample of 123 hip surgeries of a certain type, the average surgery time was 136.9 minutes with a standard deviation of 22.6 minutes. Using any method, construct a 95% confidence interval for the mean surgery time for this procedure.
(132.9,140.9)
136 ± 4.00
In an attempt to increase business on Monday nights, a restaurant offers a free dessert with every dinner order. Before the offer, the mean number of dinner customers on Monday was 150. Following are the numbers of dinners on a random sample of 12 days while the offer was in effect:
206, 169, 191, 152, 212, 139, 142, 151, 174, 220, 192, 153.
Assume the population is normally distributed. Do we reject H0 at the α=.01 significance level? State the critical value and test statistic.
Yes, we reject H0.
Critical value: 2.72
Test statistic: 3.05