Final_Review_1_Solutions

N 25 x 773 s 077 a write the hypotheses in symbols and

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Unformatted text preview: ounding variables that are not being controlled for in this study, for example the gender of the bull frog, leg length, weight, etc. 12. New York is known as “the city that never sleeps”. A random sample of 25 New Yorkers were asked how much sleep they get per night. A summary of some sample statistics are shown below. Assume that the distribution of the amount of sleep these New Yorkers get unimodal and symmetric. Based on this sample, is there significant evidence to suggest that New Yorkers on average sleep less than 8 hrs a night? n 25 x ¯ 7.73 s 0.77 (a) Write the hypotheses in symbols and in words. H0 : µ = 8 (New Yorkers on average sleep 8 hrs per night.) HA : µ < 8 (New Yorkers on average sleep less than 8 hrs per night.) (b) Are the assumptions/conditions for inference satisfied? 1. Independence Assumption: • Random Sampling Condition: We are told that the sample is random. • 10% Condition: 25 < 10% of all New Yorkers. Since we have a random sample and the 10% condition is satisfied, we can assume that the number of hours one New Yorker in the sample sleeps is independent of another. 2. Nearly Normal Condition: We are told that the distribution of the sample is unimodal and symmetric, hence we can assume the sample comes from a nearly normal distribution. 8 (c) Calculate the test statistic and find the p-value. The test statistic can be calculated as follows. t= x − µ0 ¯ s √ n = 7.73 − 8 0. √77 25 = −1.75 df = 25 − 1 = 24 0.025 < p − value < 0.05 (d) Interpret the p-value in context. If in fact New Yorkers on average sleep 8 hours per night, the probability of getting a random sample of 25 New Yorkers where the average amount of sleep is 7.73 hrs per night or less is between 0.025 and 0.05. (e) Based on the hypothesis test is there significant evidence to suggest that New Yorkers on average sleep less than 8 hrs a night? Since p-value < α (use α = 0.05 since not given) we reject the null hypothesis. There is sufficient evidence to suggest that New Yorkers on average sleep less than 8 hours per night. (f) Would you expect a confidence interval for the population mean of at an equivalent confidence level as the hypothesis test to include 8? Explain. No, the hypothesis test suggests that the average amount of sleep New Yorkers get is significantly lower than 8 hours per night therefore we wouldn’t expect 8 to be in the interval. 13. The previous question gives some summary statistics on the number of hours of sleep 25 randomly sampled New Yorkers get per night. (a) Calculate a 90% confidence interval for the number of hours of New Yorkers sleep on average and interpret this interval in context. Before we can calculate the confidence interval, we need to find the degrees of freedom and t∗ . df df = 25 − 1 = 24 t∗ = 1.711 df A 90% confidence interval can be calculated as follows: s 0.77 x ± t∗ √ = 7.73 ± 1.711 √ ¯ df n 25 = 7.73 ± 0.26 = (7.47, 7.99) We are 90% confident that New Yorkers on...
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This document was uploaded on 12/04/2013.

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