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STAT 121 Quiz23
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In planning a study of the birth weights of babies whose mothers did not see a doctor before delivery, a researcher states the hypotheses as
H0: x̄ = 1000 grams
Ha: x̄ < 1000 grams
What's wrong with this?
The hypotheses must be stated in terms of population parameters such as μ.
We always assume H0 is true when we compute P-value
n order to compute P-value, we must first compute the test statistic or z-score. The test statistic requires a numerical or claimed value for μ. This value is μ0 as specified in H0. Thus, by using μ0 in the formula of the test statistic, we are assuming H0 is true.
The correct answer is: True
Suppose we are testing H0: μ = 40 versus Ha: μ > 40. If α = 0.01 and P-value = 0.08, what should we conclude?
We say that we have insufficient evidence to conclude that the population mean is greater than 40.
When asked to explain the meaning of "the P-value was P = 0.03," a student says, "This means there is only a 0.03 probability that the null hypothesis is true." Is this a correct explanation?
This statement incorporates a common misconception many students have about P-value. The problem is that P-value is a probability of observing the data we did in a conditional situation. The conditional situation is that the null hypothesis is true. So P-value is a probability IF the null is true, not THAT the null is true. P-value is the probability of getting a test statistic as extreme or more extreme than observed IF (or assuming) the null hypothesis is true.
The correct answer is: No, this is a false explanation. A P-value is the probability, assuming the null hypothesis is true, that the test statistic will take a value at least as extreme as that actually observed.
A New York Times poll on women's issues interviewed 1025 women randomly selected from the United States, excluding Alaska and Hawaii. The poll found that 47% of the women said they do not get enough time for themselves. The poll announced a margin of error ± 3% for 95% confidence in its conclusions. What does this margin of error account for?
Sampling variation
From the actions listed below, which must we do first in the SOLVE step when performing inference?
Check conditions
A study of commuting times reports the travel times to work of a random sample of 20 employed adults in New York State. The sample mean is: x̄ = 31.25 minutes and the sample standard deviation is: s = 21.88 minutes. What is the standard error of the sample mean, x̄?
[s / √(n)] =[21.88 / √(20)] = 4.893. This is the standard error of x̄ and it estimates the standard deviation of the sampling distribution of x̄.
The correct answer is: 4.893
In practice, if we don't know whether the population is Normal and our sample size is less than 40, when will confidence levels and P-values be approximately correct?
he Normality condition for t procedures is satisfied if there are no outliers or more than one peak in the data—that is, unless the sample size exceeds 40.
The correct answer is: When the data is single-peaked and has no outliers.
Our bodies have a natural electrical field that is known to help wounds heal. Might lower levels speed healing? In a matched pairs experiment, the two hind limbs of 28 newts were razor cut and then one limb was randomly selected to receive the treatment and the other limb did not receive any treatment. The treatment consisted of a voltage applied to the limb to reduce the electrical field to half its natural value. The response was the healing rate in micrometers per hour at which new cells closed a razor cut in each limb. Which of the following states the research question?
Is the mean healing rate faster for razor cut limbs where the electrical field was reduced than for razor cut limbs that were not treated?
What happens when the equality of three means is tested by performing three separate two-sample t tests?
The overall α for all tests combined is inflated.
The more tests one performs, the greater the probability of rejecting at least one true null hypothesis. Thus, performing three or more significance tests inflates the overall type I error rate.
A random sample of 1100 teenagers (ages 12 to17) were asked whether they played games online; 775 said that they did.
Which of the following best describes the population ?
The population of interest is "all teenagers." The response is whether they play games online. This categorizes the individuals in the population rather than defining the population.
The correct answer is: All teenagers
On election day in 2004, 51% of the voters in the United States voted for George W. Bush. If a sampling distribution of p^ were predicted for random samples of 900 voters, what would be its mean?
The mean of the sampling distribution of p^ equals the population proportion regardless of sample size. So, the mean equals p=0.51.
The correct answer is: Exactly equal to p=0.51
In the 2004 Utah election, 45% of all Utah voters voted for Initiative 1. Suppose a student decided to predict the theoretical sampling distribution of p^ for samples of size 1000. Another student decides to predict the theoretical sampling distribution of p^ only she wants to predict for samples of size 1500. How will the means of these two sampling distributions for p^ compare?
The mean of the sampling distribution of p^ equals the population proportion regardless of sample size. So, the means of both sampling distributions will equal p=0.45.
The correct answer is: Both means will equal p=0.45.
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