I am having a bit of trouble with some of the questions. Some of the ones I put below have an answer, is there anyway you can check the answer and help me with the rest I am having trouble with.
Your sociology teacher claims that 60 percent of American males are married. You believe the percentage is higher. In a random sample of 973 American males, 65.8% of them were married. Is this evidence that your sociology teacher's claim is false? 1. Choose the appropriate null and alternative hypotheses for this problem:
a. Null: 65.8% of American males are married Alternative: Fewer than 65.8% of American males are married
b. Null: 60% of American males are married Alternative: Fewer than 60% of American males are married
c. Null: 60% of American males are married Alternative: More than 60% of American males are married
d. Null: 65.8% of American males are married Alternative: More than 65.8% of American males are married
I think it is C
2. The test statistic for this hypothesis test is closest to:
a. 11.8
b. 5.8
c. 3.7
d. 1.3
3. The p-value for this hypothesis is closest to:
a. 9.7%
b. 0.01%
c. 35.6%
d. 1.1%
4. Choose the correct conclusion.
a. It is very unlikely that the null hypothesis is true. (Reject the null hypothesis.)
b. The null hypothesis is likely to be true. (Accept the null hypothesis.)
c. The alternative hypothesis is definitely true. (Accept the alternative hypothesis.)
d. It is very unlikely that the alternative hypothesis is true. (Reject the alternative hypothesis.)
Use the information below to answer questions 5-7.
Dr. Jones claims that 40% of his college algebra class (very large section) will drop his course by midterm. To test his claim, he selected 45 names at random and discovered that 20 of them had already dropped long before midterm.
5. The correct null and alternative hypotheses for testing the claim are:
a. null: 20 students drop by midterm alt: 45 students drop by midterm
b. null: 44% of students drop by midterm alt: 40% of students drop by midterm
c. null: more than 40% of students drop by midterm alt: fewer than 40% of students drop by midterm
d. null: 40% of students drop by midterm alt: more than 40% of students drop by midterm
6. The test statistic value for his hypothesis test is closest to
a. 0.60
b. 0.40
c. 4.40
d. 7.40
7. Based on the sample he collected, Dr. Jones can safely conclude that:
a. Exactly 44% of his students drop by midterm.
b. It is plausible that 40% of his students drop by midterm.
c. Significantly more than 40% of his students drop by midterm.
d. Significantly fewer than 40% of his students drop by midterm.
Use the information below to answer questions 8-10.
It was reported that a certain population had an average of 27. To test this claim, you selected a random sample of size 100. The computed sample average was 25 and the sample SD was 7. The null and alternative hypotheses are listed below.
Null: The average of the population is 27. Alternate: The average of the population is less than 27.
8. The computed test statistic for these hypotheses is closest to:
a. -4.1
b. -0.4
c. -28.6
d. -2.9
I think it is D
9. The computed p-value for these hypotheses is closest to:
a. 0.2%
b. 0
c. 35%
d. 2.3%
I think it is A
10. Based on the p-value, you can claim that the average of the population:
a. is likely to be equal to 27.
b. is unlikely to be equal to 27.
c. is exactly 25.
d. is likely to be equal to 25.
I think it is B
1. Correct.
2-7. I don't know how to solve without a measure of variability.
8-10. Z = (mean1 - mean2)/standard error (SE) of difference between means
SEdiff = √(SEmean1^2 + SEmean2^2)
SEm = SD/√n
If only one SD is provided, you can use just that to determine SEdiff.
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score.
From this data, 8 is wrong but close, 9 is correct, 10 is correct.
Let's go through each question and find the correct answers:
1. To determine whether the sociology teacher's claim is false, we need to set up the null and alternative hypotheses. The alternative hypothesis should reflect that the percentage is higher than what the teacher claimed. Option (c) states the correct hypotheses: Null - 60% of American males are married, Alternative - More than 60% of American males are married. Therefore, the correct answer is (c).
2. To calculate the test statistic, we need to find the difference between the sample proportion (65.8%) and the hypothesized population proportion (60%), and then divide it by the standard error. Since the test statistic is not given, we can compute it by using the formula:
\[ \text{test statistic} = \frac{(\text{Sample proportion} - \text{Population proportion})}{\text{Standard error}} \]
Given that the sample proportion is 65.8% and the population proportion is 60%, the standard error is approximately \( \sqrt{\frac{(0.6)(0.4)}{973}} \).
After calculation, the test statistic value is closest to 5.8. Therefore, the correct answer is (b).
3. The p-value indicates the probability of obtaining results as extreme as the ones observed in the sample, assuming the null hypothesis is true. To find the p-value, we need to use the test statistic in a statistical table or software. A p-value of closest to 0.01% indicates that the observed sample proportion is highly unlikely to occur if the null hypothesis is true. Therefore, the correct answer is (b).
4. The conclusion is based on the p-value. Since the p-value is very low (closest to 0.01%), we reject the null hypothesis. Therefore, we can conclude that it is very unlikely that the null hypothesis is true. The correct answer is (a).
5. To set up the correct null and alternative hypotheses, we need to reflect Dr. Jones' claim and the corresponding alternatives. In this case, the claim is that 40% of his college algebra class will drop the course by midterm. The correct hypotheses, reflecting this claim, are: Null - 40% of students drop by midterm, Alternative - More than 40% of students drop by midterm. Therefore, the correct answer is (d).
6. The test statistic can be calculated using the formula:
\[ \text{test statistic} = \frac{(\text{Sample proportion} - \text{Population proportion})}{\text{Standard error}} \]
The sample proportion is 20/45, and the population proportion is 40%. The standard error can be calculated as \( \sqrt{\frac{(0.4)(0.6)}{45}} \). After calculation, the test statistic value is closest to 7.40. Therefore, the correct answer is (d).
7. Based on the test statistic, the p-value, which indicates the likelihood of obtaining the observed results under the null hypothesis, we can conclude that it is highly unlikely that fewer than 40% of students drop by midterm. Therefore, Dr. Jones can safely conclude that significantly more than 40% of his students drop by midterm. The correct answer is (c).
8. To compute the test statistic, we need to use the formula:
\[ \text{test statistic} = \frac{(\text{Sample mean} - \text{Population mean})}{(\text{Sample SD}/\sqrt{\text{Sample size}})} \]
Given that the sample mean is 25, the population mean is 27, the sample SD is 7, and the sample size is 100, after calculation, the test statistic value is closest to -2.9. Therefore, the correct answer is (d).
9. The p-value is the probability of obtaining results as extreme as the observed sample mean (or more extreme) when the null hypothesis is true. A p-value of closest to 0.2% suggests that the observed sample mean is highly unlikely to occur if the null hypothesis is true. Therefore, the correct answer is (a).
10. A low p-value (closest to 0.2%) suggests that the observed sample mean of 25 is unlikely to be equal to the null hypothesis mean of 27. Therefore, based on the p-value, we can claim that the average of the population is unlikely to be equal to 27. The correct answer is (b).
I hope this helps clarify the correct answers! Let me know if you have any more questions.