Assume that the amounts of weight that male college students gain during their freshman year are normally distributed with a mean of μ = 1.3 kg and a standard deviation of o=5.5 kg. Complete parts (a) through (c) below. a. If 1 male college student is randomly selected, find the probability that he gains between 0 kg and 3 kg during freshman year. The probability is (Round to four decimal places as needed.) b. If 9 male college students are randomly selected, find the probability that their mean weight gain during freshman year is between 0 kg and 3 kg. The probability is (Round to four decimal places as needed.) c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30? OA. Since the distribution is of sample means, not individuals, the distribution is a normal distribution for any sample size. OB. Since the weight gain exceeds 30, the distribution of sample means is a normal distribution for any sample size. OC. Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size. OD. Since the distribution is of individuals, not sample means, the distribution is a normal distribution for any sample size. Listed in the accompanying table are heights (in.) of mothers and their first daughters. The data pairs are from a journal kept by Francis Galton. Use the listed paired sample data, and assume that the samples are simple random samples and that the differences have a distribution that is approximately normal. Use a 0.05 significance level to test the claim that there is no difference in heights between mothers and their first daughters. Mother 64.5 63.5 66.0 62.0 62.7 64.0 64.0 60.0 62.0 65.5 Daughter 66.5 66.0 66.5 64.5 64.0 65.5 68.0 68.0 66.0 66.0 In this example, μd is the mean value of the differences d for the population of all pairs of data, where each individual difference d is defined as the daughter's height minus the mother's height. What are the null and alternative hypotheses for the hypothesis test? Ho Pa H₁: Pa in. in. (Type integers or decimals. Do not round.) Identify the test statistic. t= (Round to two decimal places as needed.) Identify the P-value. P-value = ☐ (Round to three decimal places as needed.) What is the conclusion based on the hypothesis test? Since the P-value is the significance level, the null hypothesis. There sufficient evidence to warrant rejection of the claim that there is no difference in heights between mothers and their first daughters.

Assume that the amounts of weight that male college students gain during their freshman year are normally distributed with a mean of μ = 1.3 kg and a standard deviation of o=5.5 kg. Complete parts (a) through (c) below. a. If 1 male college student is randomly selected, find the probability that he gains between 0 kg and 3 kg during freshman year. The probability is (Round to four decimal places as needed.) b. If 9 male college students are randomly selected, find the probability that their mean weight gain during freshman year is between 0 kg and 3 kg. The probability is (Round to four decimal places as needed.) c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30? OA. Since the distribution is of sample means, not individuals, the distribution is a normal distribution for any sample size. OB. Since the weight gain exceeds 30, the distribution of sample means is a normal distribution for any sample size. OC. Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size. OD. Since the distribution is of individuals, not sample means, the distribution is a normal distribution for any sample size. Listed in the accompanying table are heights (in.) of mothers and their first daughters. The data pairs are from a journal kept by Francis Galton. Use the listed paired sample data, and assume that the samples are simple random samples and that the differences have a distribution that is approximately normal. Use a 0.05 significance level to test the claim that there is no difference in heights between mothers and their first daughters. Mother 64.5 63.5 66.0 62.0 62.7 64.0 64.0 60.0 62.0 65.5 Daughter 66.5 66.0 66.5 64.5 64.0 65.5 68.0 68.0 66.0 66.0 In this example, μd is the mean value of the differences d for the population of all pairs of data, where each individual difference d is defined as the daughter's height minus the mother's height. What are the null and alternative hypotheses for the hypothesis test? Ho Pa H₁: Pa in. in. (Type integers or decimals. Do not round.) Identify the test statistic. t= (Round to two decimal places as needed.) Identify the P-value. P-value = ☐ (Round to three decimal places as needed.) What is the conclusion based on the hypothesis test? Since the P-value is the significance level, the null hypothesis. There sufficient evidence to warrant rejection of the claim that there is no difference in heights between mothers and their first daughters.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.5: Comparing Sets Of Data

Problem 14PPS

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