Question

In: Statistics and Probability

5. Suppose that researchers study a sample of 50 people and nd that 10 are left-handed....

5. Suppose that researchers study a sample of 50 people and nd that 10 are left-handed.

(a) Find a 95% confidence interval for the population proportion that is left-handed.

(b) What would the confidence interval be if the researchers used the Wilson value ~p instead?

(c) Suppose that an investigator tests the null hypothesis that the population proportion is 18% against the alternative that it is less than that. If = 0:05 then nd the critical value ^pc. Using ^p as the sample estimate, would the investigator reject the null?

(d) Suppose that researchers are using this critical value but, unbeknownst to them, the true, population proportion is 0.16. Find the power of the test.

Solutions

Expert Solution

It is a problem of one sample proportion test with a left tail alternative. Here we also find the confidence interval. All the required theoretical explanations are given in the solution.


Related Solutions

5. Suppose that researchers study a sample of 50 people and find that 10 are left-handed....
5. Suppose that researchers study a sample of 50 people and find that 10 are left-handed. (a) Find a 95% confidence interval for the population proportion that is left-handed. (b) What would the confidence interval be if the researchers used the Wilson value p ̃ instead? (c) Suppose that an investigator tests the null hypothesis that the population proportion is 18% against the alternative that it is less than that. If α = 0.05 then find the critical value pˆc....
5. Suppose that researchers study a sample of 50 people and find that 10 are left-handed....
5. Suppose that researchers study a sample of 50 people and find that 10 are left-handed. (a) Find a 95% confidence interval for the population proportion that is left-handed. (b) What would the confidence interval be if the researchers used the Wilson value ̃p instead? (c) Suppose that an investigator tests the null hypothesis that the population proportion is 18% against the alternative that it is less than that. If α = 0.05 then find the critical value ˆpc. Using...
Suppose that researchers study a sample of 50 people and find that 10 are left-handed. (a)...
Suppose that researchers study a sample of 50 people and find that 10 are left-handed. (a) Find a 95% confidence interval for the population proportion that is left-handed. (b) What would the confidence interval be if the researchers used the Wilson value ~p instead? (c) Suppose that an investigator tests the null hypothesis that the population proportion is 18% against the alternative that it is less than that. If = 0:05 then nd the critical value ^pc. Using ^p as...
Suppose that researchers study a sample of 50 people and find that 10 are left-handed. (a)...
Suppose that researchers study a sample of 50 people and find that 10 are left-handed. (a) Find a 95% confidence interval for the population proportion that is left-handed. (b) What would the confidence interval be if the researchers used the Wilson value ̃p instead? (c) Suppose that an investigator tests the null hypothesis that the population proportion is 18% against the alternative that it is less than that. If α = 0.05 then find the critical value ˆpc. Using ˆp...
. Approximately 10% of all people are left-handed, then the rest of people are right-handed. Consider...
. Approximately 10% of all people are left-handed, then the rest of people are right-handed. Consider a group of 15 people, answer the following question: (You cannot use the binomial table for this problem) (a) State the random variable ?. (2 points) (b) Explain why this is a binomial experiment. There should be 4 conditions to check. (State the probability of left-handed people ?, the possible outcomes, and the number of trials ? in the conditions.) (4 points) (c) Find...
Do left-handed people live shorter lives than right-handed people? A study of this question examined a...
Do left-handed people live shorter lives than right-handed people? A study of this question examined a sample of 949 death records and contacted next of kin to determine handedness. Note that there are many possible definitions of "left-handed." The researchers examined the effects of different definitions on the results of their analysis and found that their conclusions were not sensitive to the exact definition used. For the results presented here, people were defined to be right-handed if they wrote, drew,...
Assume that 73% of people are left-handed. If we select 5 people at random, find the...
Assume that 73% of people are left-handed. If we select 5 people at random, find the probability of each outcome described below, rounded to four decimal places: a. There are some lefties (≥ 1) among the 5 people. b. There are exactly 3 lefties in the group. c. There are at least 4 lefties in the group. d. There are no more than 2 lefties in the group. e. How many lefties do you expect? f. With what standard deviation?
Assume that 37% of people are left-handed. If we select 5 people at random, find the...
Assume that 37% of people are left-handed. If we select 5 people at random, find the probability of each outcome described below, rounded to four decimal places: a. There are some lefties ( ≥ 1) among the 5 people. b. There are exactly 3 lefties in the group. c. There are at least 4 lefties in the group. d. There are no more than 2 lefties in the group. e. How many lefties do you expect? f. With what standard...
Assume that 51% of people are left-handed. If we select 5 people at random, find the...
Assume that 51% of people are left-handed. If we select 5 people at random, find the probability of each outcome described below, rounded to four decimal places: a. There are some lefties (≥ 1) among the 5 people. b. There are exactly 3 lefties in the group. c. There are at least 4 lefties in the group. d. There are no more than 2 lefties in the group. e. How many lefties do you expect? f. With what standard deviation?
Assume that 57% of people are left-handed. If we select 5 people at random, find the...
Assume that 57% of people are left-handed. If we select 5 people at random, find the probability of each outcome described below, rounded to four decimal places: a. There are some lefties (≥ 1) among the 5 people. b. There are exactly 3 lefties in the group. c. There are at least 4 lefties in the group. d. There are no more than 2 lefties in the group. e. How many lefties do you expect? f. With what standard deviation?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT