1. For the following research question, specify the parameter and give the null and alternative hypotheses. "Is there a difference in the proportions of male and female college students who smoke cigarettes?
2. For the following research question, specify the parameter and give the null and alternative hypotheses. "Do a majority of Americans between the ages of 18 and 30 think the use of marijuana should be legalized?"
3. For the following research question, specify the parameter and give the null and alternative hypotheses. "Is the mean age of death for left-handed people lower than it is for right-handed people?
4. Suppose H0: mu1-mu2 = 0, t= -2.306, df=8, p-value=0.025. What was the alternative hypothesis for this test?
5. Suppose H0: mu1-mu2 = 0, t=2.306, df=8, p-value=0.05. What was the alternative hypothesis for this test?
6. Suppose H0: mu1-mu2 = 0, t=2.306, df=8, p-value=0.975. What was the alternative hypothesis for this test?
7. Suppose H0: mu1-mu2 = 0, t= -2.306, df=8, p-value=0.975. What was the alternative hypothesis for this test?
8. Suppose H0: mu_d = 0, d-bar = -4, s_d = 15, and n = 50. Calculate the test statistic t.
9. Suppose H0: p1-p2 = 0; HA: p1-p2 > 0; z=1.75. Find the p-value for this test.
10. Suppose H0: p1-p2 = 0; HA: p1-p2 does not equal 0; z= -1.75. Find the p-value for this test.
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1. For the research question "Is there a difference in the proportions of male and female college students who smoke cigarettes?", the parameter is the difference in proportions between male and female college students who smoke cigarettes. The null hypothesis (H0) would state that there is no difference in proportions, while the alternative hypothesis (HA) would state that there is a difference in proportions.
H0: p1 = p2 (where p1 represents the proportion of male college students who smoke cigarettes, and p2 represents the proportion of female college students who smoke cigarettes)
HA: p1 ≠ p2 (there is a difference in proportions)
2. For the research question "Do a majority of Americans between the ages of 18 and 30 think the use of marijuana should be legalized?", the parameter is the proportion of Americans between the ages of 18 and 30 who think the use of marijuana should be legalized. The null hypothesis would state that the proportion is equal to or less than 0.5 (indicating that less than or equal to 50% think marijuana should be legalized), while the alternative hypothesis would state that the proportion is greater than 0.5 (indicating that more than 50% think marijuana should be legalized).
H0: p ≤ 0.5
HA: p > 0.5 (a majority of Americans between 18 and 30 think marijuana should be legalized)
3. For the research question "Is the mean age of death for left-handed people lower than it is for right-handed people?", the parameter is the mean age of death. The null hypothesis would state that the mean age of death is equal to or greater than the mean age of death for right-handed people, while the alternative hypothesis would state that the mean age of death is lower.
H0: μ1 ≥ μ2 (where μ1 represents the mean age of death for left-handed people, and μ2 represents the mean age of death for right-handed people)
HA: μ1 < μ2 (the mean age of death for left-handed people is lower)
4. The alternative hypothesis for the given test is that the difference between the population means (mu1 and mu2) is not equal to 0.
HA: mu1-mu2 ≠ 0
5. The alternative hypothesis for the given test is that the difference between the population means (mu1 and mu2) is not equal to 0.
HA: mu1-mu2 ≠ 0
6. The alternative hypothesis for the given test is that the difference between the population means (mu1 and mu2) is not equal to 0.
HA: mu1-mu2 ≠ 0
7. The alternative hypothesis for the given test is that the difference between the population means (mu1 and mu2) is not equal to 0.
HA: mu1-mu2 ≠ 0
8. To calculate the test statistic t, you can use the formula t = (d-bar - 0) / (s_d / sqrt(n)), where d-bar is the sample mean of the differences, s_d is the standard deviation of the differences, and n is the sample size.
In this case, the test statistic t would be calculated as t = (-4 - 0) / (15 / sqrt(50)). Simplifying the calculation, t = -4 / (15 / 7.071). Thus, the test statistic t is approximately -1.885.
9. To find the p-value for this test, you would need a z-table or statistical software. Since the alternative hypothesis states that p1-p2 > 0 (a one-sided test), the p-value would be the probability of observing a z-value larger than 1.75.
Using a z-table or statistical software, you can find the cumulative probability (p-value) associated with a z-value of 1.75. The p-value would represent the probability of observing a difference between the proportions (p1-p2) larger than 1.75.