stats quick check
What is the most typical form of a calculated confidence interval Point estimate ± Margin of error Point estimate ± Standard error Population parameter ± Margin of error Population parameter ± Standard error
Point estimate ± Margin of error
A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exceeds 3.50. A sample of 36 honors students is taken and is found to have a mean GPA equal to 3.60. To establish whether the mean GPA exceeds 3.50, the appropriate hypotheses are 𝐻0:𝜇≥3.50;𝐻1:𝜇<3.50 H0:x¯≤3.50; 𝐻1:𝑥¯>3.50 𝐻0:𝜇≤3.50;𝐻1:𝜇>3.50 H0:μ<3.50; 𝐻1:𝜇≥3.50
𝐻0:𝜇≤3.50;𝐻1:𝜇>3.50
Which of the following represents an appropriate NULL hypothesis in the lower tail test? 𝐻0:𝜇<0 𝐻0:𝜇≤0 𝐻0:𝜇≥0 𝐻0:𝜇>0
𝐻0:𝜇≥0
When the p-value is used for hypothesis testing, the null hypothesis is rejected if It depends on the type of the test 𝑝−value>𝛼 𝑝−value≤𝛼 𝑝−value=1−𝛼
𝑝−value≤𝛼
Which is the following represents an estimate? 𝑝 x¯ 𝑠=3 𝜇=3
𝑠=3
A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exceeds 3.50. A sample of 36 honors students is taken and is found to have a mean GPA equal to 3.60. The population standard deviation is assumed to equal 0.40. The value of the test statistic is 𝑧𝑥¯=-1.50 𝑧𝑥¯=1.50 𝑧𝑥¯=-0.9 𝑧𝑥¯=0.9
𝑧𝑥¯=1.50
When s is used to estimate the confidence interval for the mean, the margin of error is computed by using the t distribution the mean of the population the normal distribution the mean of the sample
the t distribution
On the basis of sample information, we can either "accept the null hypothesis" or "reject the null hypothesis". True False
False
A point estimator refers to an estimator that provides a single value. True False
True
In a one-tail test, the rejection region is located under one tail (upper or lower) of the corresponding sampling distribution, while in a two-tail test this region is located under both tails. True False
True
In the hypothesis tests, the null hypothesis is believed to be true unless there is overwhelming evidence to the contrary. True False
True
When a statistic is used to estimate a parameter, the statistic is referred to as an estimator. A particular value of the estimator is called an estimate. True False
True
What type of error occurs if you fail to reject H0 when, in fact, it is not true? Type I Type II either Type I or Type II, depending on the level of significance either Type I or Type II, depending on whether the test is one-tail or two-tail
Type II
Which of the following types of tests about the population parameter may be performed? Upper-tail and lower-tail tests Upper-tail and two-tail tests Lower-tail and two-tail tests Upper-tail, lower-tail, and two-tail tests
Upper-tail, lower-tail, and two-tail tests
Consider the following hypotheses that relate to the medical field: H0: A person is free of disease H1: A person has disease In this example, when the Type I error is commited, we conclude that a truly sick person has a disease a truly healthy person has a disease a truly healthy person does not have a disease a truly sick person does not have a disease
a truly healthy person has a disease
The alternative hypothesis typically contests the status quo states the probability of rejecting the null hypothesis when it is false corresponds to the presumed default state of nature states the probability of rejecting the null hypothesis when it is true
contests the status quo
As the confidence level decreases, the confidence interval becomes wider or narrow depending on whether the population standard deviation is known or not stays the same wider narrow
narrow
As the sample size n increases, the confidence interval becomes stays the same wider wider or narrow depending on whether the population standard deviation is known or not narrower
narrower
Which is the following represents an estimator? 𝜎2 𝑠2 𝑝=0.4 𝜇
s2
For the confidence interval of the mean when the population standard deviation is known and the sample is large, the proper distribution to use is the t distribution with n degrees of freedom the t distribution with n - 1 degrees of freedom the binomial distribution the standard normal distribution
the standard normal distribution
When conducting a hypothesis test for the population mean when the population standard deviation is known, the critical value and the p-value are computed using the t-distribution the standard normal distribution the binomial distribution different distributions depending on the test
the standard normal distribution
The confidence intervals for the population proportion are generally based on the t distribution the z distribution when the sample size is very small the t distribution when the population standard deviation is not known the z distribution
the z distribution
A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exceeds 3.50. A sample of 36 honors students is taken and is found to have a mean GPA equal to 3.60. The population standard deviation is assumed to equal 0.40. To establish whether the mean GPA exceeds 3.50, you conduct a hypothesis test. You calculate that the value of the test statistic is equal to 𝑧𝑥¯=1.5zx¯=1.5 and the critical value at a 1% significance level is equal to 𝑧𝛼=2.32zα=2.32. At the significance level of 1%, the decision is to -No conclusion can be made -reject Ho because 𝑧𝑥¯<𝑧𝛼 -not reject Ho because 𝑧𝑥¯>−𝑧𝛼 -not reject Ho because 𝑧𝑥¯<𝑧𝛼
-not reject Ho because 𝑧𝑥¯<𝑧𝛼
A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exceeds 3.50. A sample of 36 honors students is taken and is found to have a mean GPA equal to 3.60. The population standard deviation is assumed to equal 0.40. Suppose that, with the given information, you calculated that the p-value for the test is equal to 0.067. How would you interpret this p-value? -If the mean GPA was equal to 3.50, then there would be a 6.7% chance of observing a mean GPA in a sample of 36 students equal to 3.60 or more. -There is a 6.7% chance that the mean GPA is smaller 3.50. -If the mean GPA was equal to 3.50, then there would be a 6.7% chance of observing a mean GPA in a sample of 36 students equal to 3.60 or less. -There is a 6.7% chance that the mean GPA exceeds 3.50.
-If the mean GPA was equal to 3.50, then there would be a 6.7% chance of observing a mean GPA in a sample of 36 students equal to 3.60 or more.
A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exceeds 3.50. A sample of 36 honors students is taken and is found to have a mean GPA equal to 3.60. The population standard deviation is assumed to equal 0.40. To establish whether the mean GPA exceeds 3.50, you conduct a hypothesis test. Suppose you concluded that you do not reject the null at 1% significance level. How would you state the concludion "in words" in relation to this problem? -There is not enough evidence to conclude that the mean GPA is greater than 3.50. -There is enough evidence to conclude that the mean GPA is greater than 3.50. -There is not enough evidence to conclude that the mean GPA is smaller than 3.50. -There is enough evidence to conclude that the mean GPA is smaller than 3.50.
-There is not enough evidence to conclude that the mean GPA is greater than 3.50.
A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exceeds 3.50. A sample of 36 honors students is taken and is found to have a mean GPA equal to 3.60. The population standard deviation is assumed to equal 0.40. Suppose that you calculated that the p-value for the test with the given information equal to 0.067. At a 10% significance level, the decision is to -not reject Ho. So, there is not enough evidence to conclude that the mean GPA is greater than 3.50. -not reject Ho. So, there is enough evidence to conclude that the mean GPA is greater than 3.50. -reject Ho. So, there is not enough evidence to conclude that the mean GPA is greater than 3.50. -reject Ho. So, there is enough evidence to conclude that the mean GPA is greater than 3.50.
-reject Ho. So, there is enough evidence to conclude that the mean GPA is greater than 3.50.
The hypothesis statement 𝐻0:𝜇≠5 is an example of alternative hypothesis in a one-tail test alternative hypothesis in a two-tail test null hypothesis in a two-tail test null hypothesis in a one-tail test
alternative hypothesis in a two-tail test
