Question

1. Imagine a study that indicates that patients given arthroscopic debridement, arthroscopic lavage or a placebo surgery all fared equally well in terms of pain and mobility over the next two years. If, in reality, the debridement treatment generally improves performance, what type of error did they make in their conclusion?

(A) Conservative error.

(B) Liberal error.

(C) p value error.

(D) Type I error.

(E) Type II error

2. The F ratio test for equality of variances is not a great test to perform if you are genuinely concerned about the accuracy of your result (i.e., you should use better tests such as the Levene's test instead). The main weakness of the F ratio test is when which of the following is true?

(A) When the data sets are not normally distributed.

(B) When the means are very different.

(C) When the sample sizes are not equal.

(E) When the sample sizes are very large.

(E) When the variances are not equal.

3. Imagine that you collect length (i.e., SVL) data for mice from two different regions. The mice from the forest have a mean SVL of 8.9 cm whereas the mice from the fields have a mean SVL mean of 9.3 cm. If you perform a two-tailed heteroscedastic t test and the overall degrees of freedom are 23 and you obtain a t value of 1.92, what would your best conclusion be?

(A) The mice from the forest are not significantly different from the mice from the fields (0.05 < p < 0.1).

(B) The mice from the forest are significantly different from the mice from the fields (0.025 < p , 0.05).

(C) The mice from the forest are significantly different from the mice from the fields (0.05 < p < 0.1).

(D) The mice from the forest are significantly smaller from the mice from the fields (0.025 < p , 0.05).

(E) The mice from the forest are significantly smaller from the mice from the fields (0.05 < p < 0.1).

4. A researcher assumes that the mean number of red blood cells per ml of blood she collects will be 5,000,000. If she gathers several samples and conducts a two-tailed one-sample t test and obtains a mean value of 5,250,300 and a p value of 0.08, what would her best conclusion be?

(A) Her data indicates that the mean number of blood cells is different from 5,000,000.

(B) Her data indicates that the mean number of blood cells is similar to 5,000,000.

(C) She lacks convincing evidence to decide that the mean number of blood cells is different from 5,000,000.

(D) She lacks convincing evidence to decide that the mean number of blood cells is similar to 5,000,000.

(E) She may have made a type I error.

5. If you are using a table of critical t values and you accidentally use the values for more degrees of freedom than you really have which of these is true?

(A) The risk of making a type I error is increased and the risk of type II error is increased.

(B) The risk of making a type I error is increased and the risk of type II error is decreased.

(C) The risk of making a type I error is decreased and the risk of type II error is increased.

(D) The risk of making a type I error is decreased and the risk of type II error is decreased.

(E) The risk of making a type I error is the same and the risk of type II error is the same.

6. The best description of what a p value represents is which of the following?

(A) The probability that the null hypothesis is true.

(B) The probability of seeing the sample data if the null hypothesis is true.

(C) The probability of seeing the sample data if the null hypothesis is false.

(D) The probability of seeing the sample data if the alternative hypothesis is true.

(E) The probability of seeing the sample data if the alternative hypothesis is false.

7. For a given difference between two sample means, the p value associated with that difference does which of the following?

(A) Decreases as the sample sizes increase and decreases as the sample variances decrease.

(B) Decreases as the sample sizes increase and increases as the sample variances decrease.

(C) Increases as the sample sizes increase and decreases as the sample variances decrease.

(D) Depends on the sample sizes, not the sample variances.

(E) Depends on the sample variances, not the sample sizes.

8. A researcher is interested in whether a drug alters the pH of blood in users. She takes blood samples from a set of individuals before and after taking the experimental medication. Unfortunately, a small number of the sample jar labels got switched and she cannot guarantee which samples are from the same individuals in a few cases. What option below is the most correct?

(A) Because only a few labels are incorrect she can still do a paired t test, she should just use a smaller p value in her analysis.

(B) She cannot do a paired t test, but since the same people are in both samples she can analyze the data with a homoscedastic t test.

(C) She cannot do a paired t test, but she can analyze the data with a heteroscedastic t test.

(D) She cannot do a t test, but she can analyze the data with an F ratio test to answer her overall question.

(E) Since the labels are not correct she cannot do a paired t test and she needs to redo the whole experiment.

9. If the standard error of a sample is 12 and the sample size was 8, which of the following values is closest to the variance of the sample?

(A) 34

(B) 96

(C) 768

(D) 1152

(E) 9216

10. When researchers compare two distributions, they sometimes conduct a Kolmogorov–Smirnov "goodness of fit" test. In this test they calculate a value D which they then compare to critical K values from the Kolmogorov distribution based upon stochastic Brownian processes. If such a test is done and a p value obtained, which of the following is the best description of what that p value represents?

(A) p is the probability that K > D.

(B) p is the probability that the observed sample means would be that different, due to sampling error, when the sample means are really the same.

(C) p is the probability that the D value would be that large if the only observed differences between the sample distributions are due to sampling error.

(D) p is the probability that sampling error causes the sample value of D to be outside the confidence interval for K.

(E) p is the probability that the two distributions are statistically significant.

Answer 1

1. Null hypothesis, H0: Arthroscopic debridement, arthroscopic lavage or a placebo surgery are all equally effective

vs. Alternative hypothesis, H1: H0 is not true.

Since here we accept H0 but in reality H0 is not true so Type II error is committed.

Option: (E) Type II error.

2. Option: (A) When the data sets are not normally distributed.

3. p-value=2P(t>1.92|t~t23)=0.0673

Option: (A) The mice from the forest are not significantly different from the mice from the fields (0.05 < p < 0.1).

4. Since p-value=0.08>0.05 so

Option: (B) Her data indicates that the mean number of blood cells is similar to 5,000,000.

5. As degrees of freedom increases the critical region increasesw hence Type I error increases and Type II error decreases.

Hence Option: (B) The risk of making a type I error is increased and the risk of type II error is decreased.

6. Option: (B) The probability of seeing the sample data if the null hypothesis is true.

7. Option: (A) Decreases as the sample sizes increase and decreases as the sample variances decrease.