WorksheetsStatistical Significance
Total questions: 23
Worksheet time: 23mins
When performing a test about the population mean, what distribution would you need to use?
z
t
chi-square
cannot determine
When performing a test about the population proportion, what distribution would you need to use?
z
t
chi-square
cannot determine
A P-value indicates:
the probability that the null hypothesis is true
the probability that the alternative hypothesis is true
the probability of obtaining the results as extreme as ours, if the null hypothesis is true
probability of a Type I error
Identify the correct null hypothesis:
H0: p = 0.50
H0: µ ≠ 0.50
H0: p = 0.48
H0: µ = 96
Which of the following represents the appropriate null & alternative hypotheses?
The mean height of women is greater than 64"
H₀: μ > 64"
Hₐ: μ ≠ 64"
H₀: μ = 64"
Hₐ: μ > 64"
H₀: p > 64"
Hₐ: p ≠ 64"
H₀: p = 64"
Hₐ: p > 64"
Suppose the P-value for a hypothesis test is 0.0304. Using α = 0.05, what is the appropriate conclusion?
a) reject the null
b) reject the alternative
c) Accept the null
d) Fail to reject the alternative
When p-value is greater than alpha we:
Reject Ho
Accept Ha
Accept Ho
Fail to Reject Ho
Ha = 47
Ha < 47
Ha > 47
Ha ≠ 47
Ha: μ<21
Ha: p<.20
Ha: p= .21
Ha: p< .21
In a test of H0: p = 0.7 against Ha: p ≠ 0.7, a sample of size 80 produces z = 0.8 for the value of the test statistic. Which of the following is closest to the P-value of the test?
0.2090
0.2119
0.4238
0.4681
0.7881
. In a test of H0: µ = 100 against Ha: µ ≠ 100, a sample of size 10 produces a sample mean of 103 and a P-value of 0.08. Which of the following is true at the 0.05 level of significance?
There is sufficient evidence to conclude that µ ≠ 100.
There is sufficient evidence to conclude that µ = 100.
There is insufficient evidence to conclude that µ = 100.
There is insufficient evidence to conclude that µ ≠ 100.
There is sufficient evidence to conclude that µ > 103.
. Which of the following is not a required condition for performing a t-test about an unknown population mean µ ?
The data can be viewed as a simple random sample from the population of interest.
The population standard deviation σ is known.
The population distribution is Normal or the sample size is large (say n > 30).
The data represent n independent observations.
All four of the other conditions are required.
An appropriate 95% confidence interval for µ has been calculated as ( − 0.73, 1.92 ) based on n = 15 observations from a population with a Normal distribution. If we wish to use this confidence interval to test the hypothesis H0: µ = 0 against Ha: µ ≠ 0, which of the following is a legitimate conclusion?
Reject H0 at the α = 0.05 level of significance.
Fail to reject H0 at the α = 0.05 level of significance.
Reject H0 at the α = 0.10 level of significance.
Fail to reject H0 at the α = 0.10 level of significance.
We cannot perform the required test since we do not know the value of the test statistic.
Which of the following increases the power of a significance test?
Using a two-tailed test instead of a one-tailed test.
Decreasing the size of your sample.
Finding a way to increase the population standard deviation σ .
Increasing the significance level α .
Decrease the effect size.
Which of the following conditions must be met in order to use a t-procedure on these paired data?
The distribution of both pre-test scores and post-test scores must be approximately Normal.
The distribution of pre-test scores and the distribution of differences (after – before) must be approximately Normal.
Only the distribution of pre-test scores must be approximately Normal.
Only the distribution of differences (after – before) must be approximately Normal.
All three distributions—before, after, and the difference—must be approximately Normal.
Bags of a certain brand of tortilla chips claim to have a net weight of 14 ounces. Net weights actually vary slightly from bag to bag and are Normally distributed with mean µ . A representative of a consumer advocacy group wishes to see if there is any evidence that the mean net weight is less than advertised and so intends to test the hypotheses H0 :µ =14 Ha :µ <14. A Type I error in this situation would mean...
concluding that the bags are being underfilled when they actually aren’t.
concluding that the bags are being underfilled when they actually are.
concluding that the bags are not being underfilled when they actually are.
concluding that the bags are not being underfilled when they actually aren’t.
none of these
A medical researcher is working on a new treatment for a certain type of cancer. After diagnosis, the average survival time on the standard treatment is two years. In an early trial, she tries the new treatment on five subjects and finds that they have an average survival time of four years after diagnosis. Although the survival time has doubled, the results of a t-test for mean survival time are not statistically significant even at the 0.10 significance level. Which of the following is the best course of action for the researcher?
Since the test was not statistically significant, she should abandon study of this treatment and move on to more promising ones
She should reexamine her computations—it is likely that she made an error
She should increase the significance level of her test so that she rejects the null hypothesis, since the treatment clearly has a positive impact.
She should use a z-test instead of a t-test.
She should expand her research program to include more subjects—this was a very small sample.
You are testing the hypothesis that a new method for freezing green beans preserves more vitamin C in the beans than the conventional freezing method. Beans frozen by the conventional methods are known to have a mean Vitamin C level of 12 mg per serving, so you are testing 0 H versus : 12 µ = : 12 Ha µ > , where µ = the mean amount of vitamin C (in mg per serving) in beans frozen using the new method. You calculate that the power of the test against the alternative : 13.5 Ha µ = is 0.75. Which of the following is the best interpretation of this value?
The complement of the probability of making a Type I error
The probability of concluding that the true mean is 12 mg/serving when it is actually 13.5 mg/serving.
The probability of concluding that the true mean is higher than 12 mg/serving when it is actually 12 mg/serving.
The probability of concluding that the true mean is 13.5 mg/serving when it actually 12 mg/serving.
The probability of concluding that the true mean is higher than 12 mg/serving when it is actually 13.5 mg/serving.
Which of the following statements is/are correct?
I. The power of a significance test depends on the effect size.
II. The probability of a Type II error is equal to the significance level of the test.
III. Error probabilities can be expressed only when a significance level has been specified.
I and II only
I and III only
II and III only
I, II, and III
None of the above gives the complete set of correct responses.
