1. A state by state survey found that among 520 randomly selected adults 25 year
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Question
1. A state by state survey found that among 520 randomly selected adults 25 years old or older in Indiana 124 had a Bachelor's degree. The survey also found that among 346 randomly selected adults 2S years old or older in Massachusetts 139 had a Bachelor's degree. At 1% significance level test the claim that the percentage of adults 25 years old or older who have a Bachelor's degree s significantly higher in Massachusetts than in Indiana. 2. A random sample of 13 Big Mac sandwiches had a mean calorie content of 540 Calories with a standard deviation of 56 calories while a random sample of 6 In-N-out Double-Double with Onion sandwiches had a mean calories content of 330 calories with a standard deviation of 38 calories. Calorie content in Big Mac sandwiches and in Double-Double with onion sandwiches are known to be normally distributed At 5% significance level test the claim that In-N out Double Double with Onion sandwiches have lower amount of calories than Big Mac sandwiches. 3. A medical researcher wants to test the effects of calcium supplements on men's blood pressure. As part of the study. 10 men are given a calcium supplement for 12 weeks. The researcher measures the men's systole blood pressure at the beginning and at the end of the 12-week study and records the results shown below. At 10% significance level, should the researcher claim that men's systole blood pressure decreased? 4. The mean score on a science assessment for 49 randomly selected male 10" graders in California was 296.5 with a standard deviation of 28.6. The mean score for 50 randomly selected female 10^th graders in California was 288 6 with a standard deviation of 24.7. find a 95% confidence interval estimate for the mean difference in scores of al male 10^th graders and all female 10* graders m California. Based on your confidence interval, who did better? Explain. 5. In problem 3. find a 90% confidence interval estimate for the difference in mean systolic blood pressure for all men if they take the calcium supplement and it they don't.Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: PI> PM
Alternative hypothesis: PI < PM
Note that these hypotheses constitute a one-tailed test.
Formulate an analysis plan. For this analysis, the significance level is 0.01. The test method is a two-proportion z-test.
Analyze sample data. Using sample data, we calculate the pooled sample proportion (p) and the standard error (SE). Using those measures, we compute the z-score test statistic (z).
p = (p1 * n1 + p2 * n2) / (n1 + n2)
p = 0.3037
SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }
SE = 0.0319
z = (p1 - p2) / SE
z = - 5.12
where p1 is the sample proportion in sample 1, where p2 is the sample proportion in sample 2, n1 is the size of sample 1, and n2 is the size of sample 2.
Since we have a one-tailed test, the P-value is the probability that the z-score is less than - 5.12. We use the Normal Distribution Calculator to find P(z < - 5.12) = less than 0.00001
Thus, the P-value = less than 0.00001
Interpret results. Since the P-value (almost 0) is less than the significance level (0.01), we have to reject the null hypothesis.
From the above test we have sufficient evidence in the favor of the claim that Bachelor degree is significantly higher in Massachussets than in Indiana.
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