timetables. With 95% confidence what proportion of all rail passengers are in favour of the timetables? 3. A random sample of 10 items is taken and is found to have a mean weight of 60 grams and a standard deviation of 12 grams. What is the mean weight of the population, a) With 95% confidence? b) With 99% confidence? 4. An inspection department is trying to determine the appropriate sample size to use. They wish to be within 1% of the true proportion with 99% confidence. Past records indicate that the proportion defective is 3 in a 100.What sample size should they use? 5. A random sample of 10 packets was taken and found to have a mean weight of 50 grams and a standard deviation of 9 grams. What is the mean weight of the population with 99% confidence. 6.A machine fills packets with spice which are supposed to have a mean weight of 40 grams. A random sample of 36 packets is taken and the mean weight is found to be 42.4 grams with a standard deviation of 6 grams. It is required to conduct a significance test at the 5% level. 7. It is required to test the hypothesis that 50% of households have a freezer.A random sample of 400 households found that 54% of the sample had freezers. The significance level is 5%.
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### Question 3: Mean Weight of the Population with Confidence Intervals #### Part a) With 95% Confidence ** Show more…
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Kari H.
A recent study in the Journal of the American Medical Association reported the results of an experiment where 40 overweight individuals followed the Weight Watchers diet for one year. Their weight changes at the end of the year had a mean of 𝑥¯=3.1 kg with a standard deviation of 𝑠=4.7 kg. We want to use this data to test the claim that the diet has an effect, that is, that the weight change is higher than 0. 1. Which set of hypotheses should be used for testing this claim? A. 𝐻0:𝜇=3.1 vs. 𝐻𝑎:𝜇>3.1 B. 𝐻0:𝜇=0 vs. 𝐻𝑎:𝜇>0 C. 𝐻0:𝜇=0 vs. 𝐻𝑎:𝜇≠0 D. 𝐻0:𝜇=0 vs. 𝐻𝑎:𝜇<0 2. Which of the following conditions must be met for the hypothesis test to be valid? Check all that apply. A. The amount each person's weight changed must be independent of the amount other participant's weights changed. B. There must be at least 10 people who 'succeeded' on the diet and 10 who 'failed'. C. There must be at least 5 people who followed the diet for a full year. D. The weight loss measurements for people in the sample must be normally distributed. E. The sample size must be at least 30 or the population data for weight loss must be normally distributed. 3. Calculate the test statistic: 4. Calculate the p-value: 5. Calculate the effect size, Cohen's 𝑑, for this test: 𝑑̂= 6. The results of this test indicate we have a... A. small B. small to moderate C. large D. moderate to large effect size, and... A. very strong evidence B. extremely strong evidence C. little evidence D. some evidence E. strong evidence that the observed result is not due to chance, assuming the null model is true. 6. A 95% confidence interval for the mean weight change (in kg) for people on this diet is (1.6, 4.6). Which of the statements below is correct? A. There is a 95% chance that 95% of the individuals in the study who followed the diet for one year lost at least 1.6 kg. B. We can be 95% confident that the mean weight loss for the population of people for whom the sample participants are a representative sample is between 1.6 kg and 4.6 kg. C. We can be confident that 95% of the individuals who follow this diet for one year will lose between 1.6 kg and 4.6 kg.
David N.
1.A medical research team studied the number of head and neck injuries sustained by hockey players. Of the 319 players who wore a full-face shield, 195 sustained an injury. Of the 323 players who wore a half-face shield, 204 sustained an injury. Which statistical test would be most appropriate to compare the protective benefits of full vs half-face shields? a.A one sample Z test for sample proportions b.A two sample Z test for sample proportions c.A two sample t test for sample means d.A one sample t test for sample means 2.An education organization claims that the mean SAT scores for male athletes and male non-athletes at a college are different. A random sample of 26 male athletes at the college has a mean SAT score of 1783 and a standard deviation of 218. A random sample of 18 male non-athletes at the college has a mean SAT score of 2064 and a standard deviation of 186. Which test would best be used to compare SAT scores between these groups? a.A one sample Z test for sample proportions b.A two sample Z test for sample proportions c.A two sample t test for sample means d.A one sample t test for sample means 3.The distribution of systolic blood pressure (SBP) tends to be symmetric and bell-shaped for adults between the ages of 45-55. An investigator wishes to calculate a 95% confidence interval (CI) for mean SBP based on a sample of n=20 adults in this age range. Which of the following is the most appropriate formula for the upper limit of the 95% CI? a.sample mean + 2.09*SEM b.sample mean + 2.18*SEM c.sample mean - 1.99*SEM d.sample mean + 1.96*SEM 4.The mean change in muscle thickness observed after a 4-week training regimen was 4 mm, and the 95% confidence interval (CI) for mean change was (-0.5, 8.5). Which is the best scientific conclusion for the effectiveness of this regimen? a.An increase in 4 mm is impressive, so the regimen has been proven effective. b.Although a mean increase was observed, it is not statistically significant because the 95% CI includes zero change. c.The lower limit of the CI is less than zero, which means a new person undergoing this training can be expected to lose muscle thickness. d.The upper limit of the CI is greater than 8, which means that an increase of 8 mm is our best prediction for a new person undergoing this training.
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