Math 11 Elementary Statistics 7.3 Sampling Distributions and the Central Limit Theorem Example 1 A sample of size 45 will be drawn from a population with mean u 15 and standard deviation o = 3.5. Is it appropriate to use the normal distribution to find probabilities for ? Your response:
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A: From the provided information, n1=11x1=97.54s1=0.95n2=59x2=97.46s2=0.63
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A: The test statistics is t=x1-x2-(μ1-μ2)s12n1+s22n2=97.54-97.25-00.94211+0.62259=0.8822814≈0.88
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A: We want to test the hypothesis by using difference of of two means and 99% CI for population mean.
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- Answer the question in the photo. Thank YouUsing practical examples from the field of statistics, determine the following variables you expect to have a normal or nearly normal distribution. Illustrate by discussing and explaining possible reasons for your answer. Scores on a very easy test Shoe sizes of a random sample of adult women The number of apples in each of 100 full bushel baskets NB: answer all questionsif a population has a normal distribution with mean mu and standard deviation sigma, thin if sigma is replaced by s, then the statistic _____ has a _____ distribution with _____ degrees of freedom. A. s,t, n-1 b. s, normal, n-1 c. x bar, t, n-1 d. x bar, normal, n1 + n2 -2
- Is this right?View Policies Current Attempt in Progress Use a t-distribution and the given matched pair sample results to complete the test of the given hypotheses. Assume the results come from random samples, and if the sample sizes are small, assume the underlying distribution of the differences is relatively normal. Assume that differences are computed using d = X¡ - X2. Test Ho : ua = 0vs H. Ha > 0 using the paired data in the following table: Situation 1 125 156 140 175 153 148 180 135 168 157 Situation 2 120 145 142 150 160 148 160 142 162 150 Give the teststatistic and the p-value. Round youranswer for the test statistic to two decimal places and your answer for the p-value to three decimal places. test statistic = p-value = eTextbook and Media MacBook Airty and Statistics CP Fall 2021 (Harward) / Probability and Statistics CP Fall 2021 (Harward) / Unit 4 DUE 11/23 / Unit 4 Test DUE 11/23 Normal Distributions A magazine reported that on average, American drivers will be involved in 3.4 car accidents while driving over their lifetime, with a standard deviation of 0.68. Number of accidents for American drivers follows a normal distribution. Four Americans who are no longer driving were randomly selected. What is the probability that their average number of accidents while driving will be larger than 4? P(E > 125) For this problem, we were told that the distribution is normal. If the shape of the distribution was not stated, we would not have been able to use the normal distribution table to find the probability, What does the Central Limit Theorenm tell us to do to be able to normalize the distribution? Increase the sample size What is the rule of thumb for normalizing the sampling distribution of means? n> 30 Please answer all parts of…
- Distribution of sample means c and dSubject: statisticsTreatment Sham Researchers conducted a study to determine whether magnets are effective in treating back pain. The results are shown in the table for the treatment (with magnets) group and the sham (or placebo) group. The results are a measure of reduction in back pain. 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. H2 14 14 0.54 0.41 0.51 1.14 a. Use a 0.05 significance level to test the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment. What are the null and alternative hypotheses? O A. Ho: H1= H2 O B. Ho: H1= H2 H1: H1> H2 O C. Ho: H1Question Help For the following information, determine whether a normal sampling distribution can be used, where p is the population proportion, a is the level of significance, p is the sample proportion, and n is the sample size. If it can be used, test the claim. Claim: p>0.50; a=0.06. Sample statistics: p30.56, n = 150 Let q= 1-p and let q= 1-p. Anormal sampling distribution be used here, since np 2 5 and nq can 2 5. If a normal sampling distribution can be used, identify the hypotheses for testing the claim. Select the coriect choice below and, if necessary, fill in the answer boxes to complete your choice. O A. Ho p Ha ps (Round to two decimal places as needed.) 1/1) 0.13/1) O E. Ho p# Hạ p = (Round to two decimal places as needed.) (0/1) (Round to two decimal places as needed.) O F. Ho ps, H3: p> O G. Anormal sampling distribution cannot be used.Treatment Sham Researchers conducted a study to determine whether magnets are effective in treating back pain. The results are shown in the table for the treatment (with magnets) group and the sham (or placebo) group. The results are a measure of reduction in back pain. 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. H2 25 25 0.53 0.46 0.93 1.01 O C. Ho: H1=H2 H1: Hy # H2 O D. Ho: H1 H2 H: H1Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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