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WorksheetsSignificance Tests for Proportions
Total questions: 14
Worksheet time: 32mins
The average yield of a certain crop is 10.1 bushels per plant. A biologist claims that a new fertilizer will result in a greater yield. The appropriate null and alternative hypotheses would be:
H0 : µ = 10.8; Ha: µ > 10.8
H0 : µ = 10.8; Ha: µ ≠ 10.8
H0 : µ = 10.1; Ha: µ > 10.1
H0 : µ = 10.1; Ha: µ < 10.1
H0 : µ = 10.1; Ha: µ ≠ 10.1
An opinion poll asks a SRS of 200 adults how they feel about voting for an amendment. What hypothesis would test if the proportion is greater than 60%?
H0 : p = 0.6; Ha: p > 0.6
H0 : p = 0.6; Ha: p ≠ 0.6
H0 : p = 0.6; Ha: p < 0.6
H0 : p = 0.6; Ha: p = 0.75
H0 : p = 0.75; Ha: p < 0.6
A test of significance produces a P-value of 0.035. Which of the following conclusions is appropriate?
Accept Ha at the α = 0.05 level
Reject Ha at the α = 0.01 level
Fail to reject H0 at the α = 0.05 level
Reject H0 at the α = 0.05 level
Accept H0 at the α = 0.05 level
Type II error is
rejecting the null hypothesis when it is true
failing to reject the null hypothesis when it is false
rejecting the null hypothesis when it is false
failing to reject the null hypothesis when it is true
more serious than a Type I error
A researcher plans to conduct a significance test at the significance level of 0.05. She designs her study to have a power of 0.85 for a particular alternative value of the parameter. The probability that the researcher will commit a Type II error for the particular alternative value of the parameter at which she computed the power is
0.05
0.15
0.80
0.95
equal to the 1 - (P-value) and cannot be determined until the data have been collected
In hypothesis testing, β is the probability of committing a Type II error in a test with significance level α. The probability of committing a Type I error is
1 - β
1 - α
β - α
α
cannot be determined
James, a claimed psychic, was presented with 200 cards face down and was asked to determine if the card was one of 5 symbols. He was correct in 50 cases. When testing the hypotheses H0: p= 0.20 and Ha: p>0.20 and assuming conditions are met, the P-value of this test is
between 0.10 and 0.05
between 0.05 and 0.025
between 0.025 and 0.01
between 0.01 and 0.001
below 0.001
The most important condition for drawing sound conclusions from statistical inference is usually
that the population standard deviation is known
that at least 30 people are included in the study
that the data come from a random sample or a randomized experiment
that the population distribution is exactly Normal
that no calculation errors are made in the confidence interval or test statistic
It is believed that a mean weight of 160 pounds would be normal for a type of athletes. To see if there is evidence that the mean weight of the population of all athletes is significantly higher than 160 pounds you test the hypotheses H0: μ = 160; Ha: μ > 160 and obtain a P-value of 0.0742. Which of the following is true?
At the 5% significance level, you have proved H0 is true.
You have failed to obtain sufficient evidence against H0.
At the 5% significance level, you have failed to prove that H0 is true, and a larger sample size is needed to do so.
Only 7.42% of the athletes weigh less than 160 pounds.
None of the above. A significance test is inappropriate in this setting.
A rubber band man claims that p, the proportion of bands that snap when stretched beyond 8 inches, is no more than 0.03. Some customers have complained that this happens more frequently. Which of the following sets of hypotheses would the customers used to conduct an experiment to test the rubber band man's claim?
H0: p ≠ 0.03, HA: p = 0.03
H0: p = 0.03, HA: p > 0.03
H0: p = 0.03, HA: p ≠ 0.03
H0: p = 0.03, HA: p < 0.03
H0: p > 0.03, HA: p = 0.03
There is a law in ND saying that the ratio of elementary students to teachers can be no more than 22:1. A hypothesis test is performed to determine if the proportion of schools is above 25% using an SRS of 85 schools. At the 0.05 significance level, what conclusion can be made if 32 of the schools surveyed exceed this ratio?
Since the p-value is less than the level of significance level, the null hypothesis should be rejected. There is significant evidence that the true proportion of schools with a higher ratio of more than 25%.
Since the p-value is greater than the level of significance level, the null hypothesis should be rejected. There is significant evidence that the true proportion of schools with a higher ratio of more than 25%.
Since the p-value is less than the level of significance level, the null hypothesis should not be rejected. There is not significant evidence that the true proportion of schools with a higher ratio of more than 25%.
Since p-hat = 0.376 > 0.05, the null hypothesis should not be rejected. There is not significant evidence that the true proportion of schools with a higher ratio is greater than 25%.
Since p-hat = 0.376 > 0.05, the null hypothesis should be rejected. There is significant evidence that the true proportion of schools with a higher ratio is greater than 25%.
In a random of 850 city high school students, 768 said they had access to the internet during school hours. 308 of 355 rural high school students said they had access. which of the following is the p-value for a significance test to determine if these data provide evidence that the proportion of high school students in city areas who have internet access is different than those who go to rural schools?
0.002
0.011
0.022
0.033
0.066
A nutritionist claims U.S. children drink an average of less than 2 glasses of milk per day. Based on an SRS of 30 children, the p-value of H0: μ = 2 vs. HA: μ < 2 is 0.0015. What is the correct interpretation of the p-value?
The probability that she fails to reject the null hypothesis is 0.015%
The probability that she rejects the null is 0.015%
She can be 99.85% confident that the alternative hypothesis is true
About 0.15% of all samples would product a test statistics at least as extreme as ours if the null hypothesis is true.
About 99.85% of all samples would product a test statistics at least as extreme as ours if the null hypothesis is true.
The process of making cough drops yields drops with varying amounts of the active ingredient. It is claimed that the average amount of this ingredient per tablet is at least 400mg. We test a random sample of 90 tablets. The mean content of the active ingredient for the sample is 396.8mg, while the standard deviation is 31mg. What is the approximate p-value for the appropriate test?
0.050
0.100
0.165
0.330
0.335
