For the following, decide whether the statement is true or false and explain why
ID: 3318961 • Letter: F
Question
For the following, decide whether the statement is true or false and explain why. (One or two sentences explaining your reasoning)
a. If the correlation between X and Y is 0.82, then for any given X observation that is small (i.e., below the average X value), its corresponding Y observation is also small (i.e., below the average Y value)
b. Suppose we want to construct a 95% confidence interval using repeated sampling of 100 samples. Because the population mean () is a random variable, the specific values for the 95% confidence intervals will vary across those 100 samples.
c. The daily sales for a local hardware store is known to follow a probability distribution with a mean of $1230 and a standard deviation of $445. Suppose Leland takes a random sample of fifteen daily sales. The approximate shape of the sampling distribution of the sample mean for daily sales is unknown
d. The U.S. Food and Drug Administration (FDA) requires that all potential new drugs be tested to see whether they are actually effective before they can be released to the public. In essence, they are testing a null hypothesis that the drug is ineffective versus the alternative hypothesis that the drug is effective. Suppose the FDA decides to change the significance level on this test from 0.05 to 0.01. Relative to the 0.05 level of significance, the adoption of the 0.01 criterion will mean that there will be a reduction in the number of effective and ineffective drugs that are released.
e. Relative to a non-random sample, a random sample with the same sample size can be expected to yield an estimate of the population parameter that has less variability
f. Katie is trying to determine whether a coin is fair. She flips the coin 100 times and counts the number of times heads came up. She then computes a z-test statistic of 0. Katie's z-test statistic indicates that she must necessarily have observed the same number of heads as tails.
g. Ray wants to choose the histogram that best represents 200 rolls of a fair six-sided die. He is shown four histograms. The first histogram depicts a negatively skewed distribution, the second depicts a positively skewed distribution, the third depicts a normal distribution, and the fourth depicts a uniform distribution. He should choose the histogram depicting a normal distribution.
h. Many factors affect the rejection region for a hypothesis test. One of those factors is the p-value.
Explanation / Answer
a. If the correlation between X and Y is 0.82, then for any given X observation that is small (i.e., below the average X value), its corresponding Y observation is also small (i.e., below the average Y value)
Yes becuase correlation coeffcient between the variables is positive. So as X decreases Y will also decrease.
b. Suppose we want to construct a 95% confidence interval using repeated sampling of 100 samples. Because the population mean () is a random variable, the specific values for the 95% confidence intervals will vary across those 100 samples.
Yes it is true becuase sample mean will vary from one sample to other sample.
c. The daily sales for a local hardware store is known to follow a probability distribution with a mean of $1230 and a standard deviation of $445. Suppose Leland takes a random sample of fifteen daily sales. The approximate shape of the sampling distribution of the sample mean for daily sales is unknown
Yes it is true becuase sample size is less than 30.
d. The U.S. Food and Drug Administration (FDA) requires that all potential new drugs be tested to see whether they are actually effective before they can be released to the public. In essence, they are testing a null hypothesis that the drug is ineffective versus the alternative hypothesis that the drug is effective. Suppose the FDA decides to change the significance level on this test from 0.05 to 0.01. Relative to the 0.05 level of significance, the adoption of the 0.01 criterion will mean that there will be a reduction in the number of effective and ineffective drugs that are released.
Reduction in signficance level means that we increases the chance of accepting null hypothesis.
Hence, it is false.
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