A. Directions: Study the table below. Find the critical value, draw the rejection region, compute the value of the test statistic, and state your decision whether to accept or reject the null hypothesis in each of the following situations. Hypotheses Given Rejection Region Test Value Decision X = 11.5 Ho: μ = 14 Ha: μ = 14 s = 5.5 n = 35 α = 0.01 X = 75 Ho: μ = 80 Πα: μ < 80 0² = 25 n = = 20 α = 0.01 X = 10 Ho: μ = 9.8 Ha: μ > 9.8 s = 4.3 n = 12 α = 0.05
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- You wish to test the following claim (H0,Ha) at a significance level of α=0.002 Ho:μ1=μ2 Ha:μ1≠μ2You obtain the following two samples of data. Sample #1 Sample #2 91.1 91.9 75.1 68.6 77.8 97 81.3 76.3 95 89.6 75.1 81.3 93.6 85.7 82.7 78.9 99.4 87.8 91.9 95.5 71.9 73.8 92.7 86.7 79.3 71.4 60.2 95 75.9 72.4 71.4 73.8 86.7 82.7 75.9 78.2 64.9 92.7 85 99.4 89.6 97 80 83.7 68.6 100.1 96.5 98.8 79.6 76.7 56.2 63.9 67.4 51.6 95.4 78.6 63.1 71.3 93.3 105.2 70.3 68 64.7 91.8 90.4 82.3 62.3 104.2 92.3 89.9 103.2 81.1 73.3 105.2 79.4 79.8 94.3 44.4 67.4 44.4 44.4 89 66.1 79 96.6 58.2 59.4 77.3 78.6 113 93.3 94.9 76.9 87.7 89.5 99.2 86 70.3 76 69.2 83.5 57 110.8 63.9 61.4 110.8 86.9 90.4 44.4 71.3 What is the test statistic for this sample? (Report answer accurate to three decimal places.)test statistic = What is the p-value for this sample? For this calculation, use the degrees of freedom reported from the…The summary statistics for a certain set of points are: n=25, s = 121.69, Σ (x-x)² =42.30, and b₁ = 24.99. Use the critical value method to test the null hypothesis Ho : B₁ = = 0 versus H₁ B₁ +0. Use the a= 0.05 level of significance. Part: 0 / 4 Part 1 of 4 Find the critical value(s). Round the answer to three decimal places. If there is more than one critical value, separate them with commas. Critical value(s): 0,0,... X +0 ŚTest the claim about the population mean, μ,at the given level of significance using the given sample statistics. Claim: μ=50; α=0.08; σ=3.95. Sample statistics: x=49.7, n=67 a. Identify the null and alternative hypotheses b. Calculate the standardized test statistic. c. Determine the critical value(s). d. Determine the outcome and conclusion of the test.
- Use the given information to find the p-value. Also, use a 0.05 significance level and state the conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis). With H 1: p≠0.377, the test statistic is z=3.06.Find the value of the standard score, z, and determine whether to reject the null hypothesis at a 0.01 significance level. Is the alternative hypothesis supported? Ho: μ = 19.1 meters, H₂: μ# 19.1 meters, n=144, x= 18.4 meters, o = 1.4 meters The value of the standard score is (Round to two decimal places as needed.) The critical value(s) is/are (Use a comma to separate answers as needed. Round to two decimal places as needed.) Determine whether the alternative hypothesis is supported at a 0.01 significance level. O A. The standard score is at least as extreme as the critical value(s). Reject Ho. The alternative hypothesis is supported. OB. The standard score is at least as extreme as the critical value(s). Do not reject Ho. The alternative hypothesis is not supported. C. The standard score is less extreme than the critical value(s). Reject Ho. The alternative hypothesis is supported. D. The standard score is less extreme than the critical value(s). Do not reject Ho. The alternative…Test the claim about the difference between two population means u, and u, at the level of significance a. Assume the samples are random and independent, and the populations are normally distributed. Claim: µ1 = H2; a = 0.01 Population statistics: o, = 3.5, o2 = 1.4 Sample statistics: x, = 17, n, = 31, X2 = 15, n2 = 30 Determine the alternative hypothesis. Ha: H1 # H2 Determine the standardized test statistic. z= 2.95 (Round to two decimal places as needed.) Determine the P-value. P-value = (Round to three decimal places as needed.)
- Which of the following is the best decision and conclusion based on the result below? H.: p = 0.10 Ha:p + 0.10 Critical Value: +1.645 Computed Test Statistics: z = 5.61 O a. Since the computed test statistics is less than the critical value, do not reject Ho. Therefore, we conclude that at 0.10 level of significance, there is enough evidence that the population proportion is different from 10%. O b. Since the computed test statistics is less than the critical value, do not reject Ho. Therefore, we conclude that at 0.10evel of significance, there is enough evidence that the population proportion is different from 10%. O c. Since the computed test statistics is greater than the critical value, reject Ho. Therefore, we conclude that at 0.10 level of significance, there is enough evidence that the population proportion is different from 10%. O d. Since the computed test statistics is less than the critical value, reject Ho. Therefore, we conclude that at 0.10 level of significance, there…A phone company plans on offering their new smartphone in four colours: white, black, silver and rose gold. They anticipate that 30% of shoppers will prefer white, 35% will prefer black, 20% will prefer silver and 15% will prefer rose gold. They perform market research by asking a random sample of 350 potential customers which colour they prefer. Colour Frequency White 104 Chi Square ribution Table Black 127 SAMSUNG Can the company conclude that their expected distribution was accurate using a 1% level of significance? Silver 89 SUBMIT QUESTION Rose Gold ВО SAVE PROGRESS SUBMIT ASSIGNMENT 10:16 AAssume a significance level of α=0.1 and use the given information to complete parts (a) and (b) below. Original claim: The mean pulse rate (in beats per minute) of a certain group of adult males is 70 bpm. The hypothesis test results in a P-value of 0.0025. a. State a conclusion about the null hypothesis. (Reject H0 or fail to reject H0.) Choose the correct answer below. A. Fail to reject H0 because the P-value is less than or equal to α. B. Reject H0 because the P-value is less than or equal to α. C. Reject H0 because the P-value is greater than α. D. Fail to reject H0 because the P-value is greater than α. b. Without using technical terms, state a final conclusion that addresses the original claim. Which of the following is the correct conclusion? A. The mean pulse rate (in beats per minute) of the group of adult males is 70 bpm. B. There is sufficient evidence to warrant rejection of the claim that the…
- Dentists A toothpaste company wants to declare in an ad that more than 80% of dentists recommend their toothpaste. The company performs a hypothesis test at the α = 0.05 significance level to test their claim. The company samples 800 dentists. Of these, 653 recommend their toothpaste. Let p represent the population proportion of dentists that recommend their toothpaste. b.Calculate the z or t statistic. (Do not use continuity correction. Round final answer to 4 decimal places) Statistic: c. Find the p-value. (Do not use continuity correction. Round final answer to 4 decimal places) p-value:Only 16% of registered voters voted in the last election. Will voter participation increase for the upcoming election? Of the 327 randomly selected registered voters surveyed, 56 of them will vote in the upcoming election. What can be concluded at the αα = 0.05 level of significance? For this study, we should use: z-test for a population proportion or t-test for a population mean The null and alternative hypotheses would be: H0:H0: ? μ p Select an answer ≠ < = > (please enter a decimal) H1:H1: ? p μ Select an answer > = ≠ < (Please enter a decimal) The test statistic ? z or t = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.) The p-value is ? > ≤ αα Based on this, we should Select an answer: accept, reject or fail to reject the null hypothesis. Thus, the final conclusion is that ... The data suggest the population proportion is not significantly higher than 16% at αα = 0.05, so there…The NAEP considers that a national average of 283 is an acceptable performance. Using α = .05, run a two-tail t-test for one sample to test Ho: µ=283 for the 2019 scores. Report the t-obt, df, and p-values. Would you reject the null hypothesis that the 2019 scores come from a population with average 283? If this is the case, does it come from a population from larger or smaller average?