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- For a one-sample test for a population proportion pp and sample size nn, why is it necessary that np0np0 and n(1−p0)n(1−p0) are both at least 10 ? A)The sample size must be large enough to support an assumption that the distribution of the population is approximately normal. B)The sample size must be large enough to support an assumption that the distribution of the sample is approximately normal. C)The sample size must be large enough to support an assumption that the sampling distribution of the sample proportion is approximately normal. D)The sample size must be large enough to support an assumption that the observations are independent. E)The sample size must be large enough to support an assumption that the sample proportion is an unbiased estimator of the population proportion.1) A study of 29 female Sumatran elephants provided a 96% confidence t-interval for the mean shoulder height of all female Sumatran elephantsas (195.8, 235.4) cm. a) What is the reasonable point estimate for themean shoulder height of all female Sumatranelephants, µ.A. 195.8cm.B. 215.6cm.C. 235.4cm.D. All of the aboves are reasonable point estimates for µ.E. Since we don’t know the population, wecan’t estimate µ. b) Assume the margin of error is 10. Whatis the standard error (SE) of the mean?A. 4.642B. 4.651.C. 4.883.D. 4.890.E. Cannot calculate based on the given information.For a one-sample test for a population proportion and sample size , why is it necessary that andare both at least 10 ?(A) The sample size must be large enough to support an assumption that the distribution of the population isapproximately normal.(B) The sample size must be large enough to support an assumption that the distribution of the sample isapproximately normal.(C) The sample size must be large enough to support an assumption that the sampling distribution of the sampleproportion is approximately normal.(D) The sample size must be large enough to support an assumption that the observations are independent.(E) The sample size must be large enough to support an assumption that the sample proportion is an unbiasedestimator of the population proportion
- (a) What is the minimal sample size needed for a 95% confidence interval to have a maximal margin of error of 0.2 if a preliminary estimate for p is 0.38? Recall that the minimal sample size n for a given maximal margin of error when a preliminary estimate for p is known can be found using the formula n = p(1 − p) zc E 2 , where E is the maximal margin of error.We are interested in the minimal sample size for a 95% confidence interval with a maximal margin of error of 0.2. The table below lists critical values for confidence intervals at different levels of confidence. Confidence Interval Critical Values zc Level of Confidence c Critical Value zc 0.70, or 70% 1.04 0.75, or 75% 1.15 0.80, or 80% 1.28 0.85, or 85% 1.44 0.90, or 90% 1.645 0.95, or 95% 1.96 0.98, or 98% 2.33 0.99, or 99% 2.58 According to this table, for a 95% confidence level, z0.95 = 1.96. We want the confidence interval to have a maximal margin of error of 0.2 and…Given a sample of size n=20 and the sample mean of 10 and a standard deviation of 3, find the distance between the upper and lower bounds of a 99% confidence interval for the population mean.( answer in two decimals)An electrical engineer wishes to determine if, among two specific municipal buildings in town, Building “North” and Building “South”, whether the tensile strength of pipes (in psi) is not the same in each of these two buildings. A sample of pipes was chosen at random from both Building “North” and Building “South”, respectively. Using α = 0.05, which of the following statistical test, or parameter, would be best for determining whether tensile strength of pipes (in psi) is not the same in each of these two buildings? (Assume all statistical assumptions met.) a) Binomial Distribution b) Population Difference in Means (i.e., Unpaired Data) c) The Chi-Squared Test of Independence d) Population Mean Difference (i.e., Paired Data)
- Conduct a test at the α=0.01 level of significance by determining (a) the null and alternative hypotheses, (b) the test statistic, and (c) the P-value. Assume the samples were obtained independently from a large population using simple random sampling. Test whether p1>p2. The sample data are x1=129, n1=241, x2=139, and n2=312. (a) Choose the correct null and alternative hypotheses below. A. H0: p1=p2 versus H1: p1≠p2 B. H0: p1=p2 versus H1: p1>p2 Your answer is correct. C. H0: p1=p2 versus H1: p1<p2 D. H0: p1=0 versus H1: p1≠0 (b) Determine the test statistic. z0= (Round to two decimal places as needed.) Pvalue = (Round to three decimal places as needed.The amniotic fluid analysis of a simple random sample of 15 pregnant women showed the following measurements in the total protein present in grams per 100 ml. 0.69 1.04 0.39 0.37 0.64 0.73 0.69 1.04 0.83 1.00 0.19 0.61 0.42 0.20 0.79 Build a 95% confidence interval for population variance in the measurements of the total protein present in the amniotic fluid of pregnant women.Provided below are summary statistics for independent simple random samples from two populations. Use the nonpooled t-test and the nonpooled t-interval procedure to conduct the required hypothesis test and obtain the specified confidence interval. x1=11,s1=5,n1=10,x2=15,s2=6,n2=10 a. Two-tailed test,α=0.05 b.95%confidence interval a. What are the hypotheses for the t-test? A.H0:μ1=μ2 Ha:μ1>μ2 B.H0:μ1=μ2 Ha:μ1≠μ2 C.H0:μ1≥μ2 Ha:μ1<μ2 D.H0:μ1=μ2 Ha:μ1<μ2 Find the test statistic. t= (Round to three decimal places as needed.) Find the P-value. P= (Round to four decimal places as needed.) What is the conclusion of the hypothesis test? A.Reject H0.There is sufficient evidence that the two means are different. B. Do not reject H0. There is insufficient evidence that the two means are different. C.Do not reject H0. There is sufficient evidence that the two means are different. D.Reject H0.There is…
- Provided below are summary statistics for independent simple random samples from two populations. Use the nonpooled t-test and the nonpooled t-interval procedure to conduct the required hypothesis test and obtain the specified confidence interval. x1=20, s1=5,n1=15,x2=29,s2=8,n2=25 a. Left-tailed test, α=0.05 b.90%confidence interval A. What are the hypotheses for the t-test? A.H0:μ1=μ2 Ha:μ1>μ2 B. H0:μ1≤μ2 Ha:μ1>μ2 C. H0:μ1=μ2 Ha:μ1≠μ2 D. H0:μ1=μ2 Ha:μ1<μ2 Find the test statistic. t= (Round to three decimal places as needed.) Find the P-value. P= (Round to four decimal places as needed.) What is the conclusion of the hypothesis test? A. Do not reject H0. There is sufficient evidence that μ1 is less than μ2. B. Reject H0.There is insufficient evidence that μ1 is less than μ2. C.Reject H0.There is sufficient evidence that μ1 is less than μ2. D.Do not reject H0.There is insufficient evidence…Provided below are summary statistics for independent simple random samples from two populations. Use the nonpooled t-test and the nonpooled t-interval procedure to conduct the required hypothesis test and obtain the specified confidence interval. x1=10, s1=2, n1=10, x2=14, s2=6, n2=10 a. Two-tailed test, α=0.05 b. 95% confidence interval a. What are the hypotheses for the t-test? A. H0: μ1=μ2 Ha: μ1≠μ2 B. H0: μ1≥μ2 Ha: μ1<μ2 C. H0: μ1=μ2 Ha: μ1>μ2 D. H0: μ1=μ2 Ha: μ1<μ2 Find the test statistic. t=_________ (Round to three decimal places as needed.) Find the critical values. ±tα/2=±___________ (Round to three decimal places as needed.) What is the conclusion of the hypothesis test? A. Do not reject H0. There is insufficient evidence that the two means are different. B. Reject H0. There is sufficient evidence that the two means are different. C. Reject H0. There is insufficient evidence that the…Considering a treadmill test given to patients being tested for high blood pressure, male patients took their pulse rates before and after running for 5 min. (a=1) Subject 1 2 3 4 5 6 7 8 9 10 Pulse before 64 100 8a 60 92 8a 68 8a 8a 68 Pulse after 68 11a 84 68 10a 92 72 88 80 92 Using a 0.05 significance level, perform the 8-step hypothesis test to test the claim that the mean difference between the pulse rates before and after the run is significantly zero. Based on the result, do the male pulse rates taken before and after running appear to be about the same or not?
