Suppose a random sample size of 60 is taken from a population with p = 0.51. For this random sample, which of th following statements is/are true? O The sampling distribution of the sample proportions is approximately normally distributed. O Both a and b O Neither a nor b O The standard error increases as the sample size increases.
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- The sampling distributions below come from samples with a population standard deviation of 28. Which one has a sample size of 49? 1 2 3 N N N 100 103 106 109 112 115 sample mean Onone of these 0 3 01 02 118 80 84 88 92 96 100 sample mean 04 110 112 114 116 118 120 122 124 126 sample meanMen Women H1 H2 A study was done on body temperatures of men and women. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. n 11 59 97.54°F 0.78°F 97.41°F 0.64°F a. Use a 0.01 significance level to test the claim that men have a higher mean body temperature than women. What are the null and alternative hypotheses? O A. Ho: H1 = H2 H1: H1 H2 O B. Ho: H1 =H2 H1: H1> H2 OC. Ho: H1 H2 O D. Ho: H1 2 H2 H1: H12% of the world population is naturally blond. In a random sample of 100 people, the proportion of natural blonds is found. The sampling distribution of is O A. approximately normal because p is always approximately normal O B. not approximately normal because np 5Suppose that we will take a random sample of size n from a population having mean µ and standard deviation σ. For each of the following situations, find the mean, variance, and standard deviation of the sampling distribution of the sample mean: µ = 142, σ = 4, n = 1,108Listed in the accompanying table are waiting times (seconds) of observed cars at a Delaware inspection station. The data from two waiting lines are real observations, and the data from the single waiting line are modeled from those real observations. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b). One Line Two Lines 64.1 733.6 64.3 865.2 157.2 605.8 215.8 1089.7 142.2 267.8 85.6 662.7 278.9 310.2 339.6 518.1 253.2 128.8 199.5 565.6 475.7 132.9 630.3 268.2 478.2 122.1 333.1 350.4 473.5 128.9 328.9 95.2 402.1 232.7 914.6 99.7 721.6 461.2 552.8 162.7 760.7 482.2 596.7 100.6 692.3 518.1 837.1 508.5 903.1 580.2Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. A researcher was interested in comparing the GPAs of students at two different colleges. Independent simple random samples of 8 students from college A and 13 students from college B yielded the following GPAs. College A 3.7 3.2 3.0 2.5 2.7 3.6 2.8 3.4 College B 3.8 3.2 3.0 3.9 3.8 2.5 3.9 2.8 4.0 3.6 2.6 4.0 3.6 Construct a 95% confidence interval for μ1−μ2, the difference between the mean GPA of college A students and the mean GPA of college B students. Round to two decimal places. (Note: x1=3.1125, x2=3.4385, s1=0.4357 s2=0.5485Samples of size n- 9 are selected from a normal population withp -80with o- 18. What is the standard error for the distribution of sample means? OM-5 OM- 18 O M- 6 0 0Let x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with ? = 2.5%. A random sample of 10 bank stocks gave the following yields (in percents). 5.7 4.8 6.0 4.9 4.0 3.4 6.5 7.1 5.3 6.1 The sample mean is = 5.38%. Suppose that for the entire stock market, the mean dividend yield is ? = 4.9%. Do these data indicate that the dividend yield of all bank stocks is higher than 4.9%? Use ? = 0.01. (c) Find (or estimate) the P-value. (Enter a number. Round your answer to four decimal places.) ?Sketch the sampling distribution and show the area corresponding to the P-value. (Select the correct graph.)K A study was done on body temperatures of men and women. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. e this 2 Z a. Use a 0.05 significance level to test the claim that men have a higher mean body temperature than women. What are the null and alternative hypotheses? OA Ho: Hy #₂ H₂: Hy H₂ F2 淋 X command дв 3 80 F3 E D с $ 4 R F % 5 V T G 6 B MacBook Air Y H & 7 N F7 U J * 8 M OB. Ho: ₁2₂ H₁: Hy t : - ; H n X S option Clear all F11 { [ Men H₁ 11 97.64°F 0.77 F ? 1 + = 11 I Check answer 4) F12 Women H₂ 59 97.45°F 0.63°F } ] delete ▼ return shift drewIH a lårge population of fish, the proportion of angel fish is Let P be the random variable that represents the sample proportion of angel fish for samples of size n drawn from the population. Find the smallest integer value of n such that the standard deviation of P is less than or equal to 100Suppose that the random variable z has a standard normal distribution. Sketch each of the following z points, and use the normal table to find each z point. a) z(-0.01)b) z(-0.05)c) z(-0.10)A Find the standard error of the mean for each sampling situation (assuming a normal population). (Round your answers to two decimal places). 1. O=56, n=4 2. O=56, n=16 3. O=56, n=64 B. What happens to the standard error each time you quadruple the sample size? The standard error is ________ by half.
