You wish to conduct a hypothesis test to determine if a bivariate data set has a significant correlation among the two variables. That is, you wish to test the claim that there is a correlation (Ha:ρ≠0Ha:ρ≠0). You have a data set with 25 subjects, in which two variables were collected for each subject. You will conduct the test at a significance level of α=0.05α=0.05. Find the critical value for this test. rc.v. = ±± Report answers accurate to three decimal places
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You wish to conduct a hypothesis test to determine if a bivariate data set has a significant
Find the critical value for this test.
rc.v. = ±±
Report answers accurate to three decimal places
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- Suppose a company claims that its market share is less than 16 percent, on average. Several of coworkers do not believe this, so a director decides to do a hypothesis test, at a 1% significance level, to persuade them. He conducts 21 surveys, collects the proper data, and works through the testing procedure: H0: μ≥16; Ha: μ<16 x¯=15.8 σ=1.8 α=0.01 (significance level) The test statistic is z0=x¯−μ0σn√=15.8−161.821√=−0.51 The critical value is −z0.01=−2.33. Conclude whether to reject or not reject H0, and interpret the results. Select the correct answer below: Reject H0. At the 1% significance level, the test results are not statistically significant and at best, provide weak evidence against the null hypothesis. Reject H0. At the 1% significance level, the data provide sufficient evidence to conclude that the mean market share is less than 16 percent. Do not reject H0. At the 1% significance level, the test results are not statistically significant…The test statistic of z = -2.27 is obtained when testing the claim that p < 0.32 Part A: using a significance level a= 0.10, find the critical value(s)As we have noted in previous chapters, even a very small effect can be significant if the sample is large enough. Suppose, for example, that a researcher obtains a correlation (computed from the raw data) of r = 0.60 for a sample of n = 10 participants. (4 pts. total) Is this sample sufficient to conclude that a significant correlation exists in the population? Use a two-tailed test with α = .05. In your response, be sure to specify the critical value for r.
- Based on research with her patients, Dr. Sabine knows that the correlation coefficient between scores on an anxiety scale and comfort at a social gathering is –0.35. If the critical value for r is 0.330, what should she conclude? a. The null hypothesis should be retained. b. Scores on the anxiety scale are significantly related to feelings of comfort in a social gathering. c. Scores on the anxiety scale are not significantly related to feelings of comfort in a social gathering. d. Scores on the anxiety scale are causally related to feelings of comfort in a social gathering.A nationwide study of undergraduate students reported that the mean number of drinks consumed per week during the spring semester is 7.96. The mean number of drinks consumed per week at USC is 7.64 (s.d.=2.55, N=412 Health services is concerned that USC students are consuming significantly more alcohol per week than the national average. Using an alpha level of .05, Is there sufficient evidence to be concerned? Be sure to select the correct critical value for the alternative hypothesis, and then use this evidence to make your conclusionSuppose you will perform a test to determine whether there is sufficient evidence to support a claim of a linear correlation between two variables. Find the critical values of r given n = 11 at a significance level of 0.05. ±± 0.575 ±± 0.514 ±± 0.555 ±± 0.602
- In a completely randomized experimental design, three brands of paper towels were tested for their ability to absorb water. Equal-size towels were used, with four sections of towels tested per brand. The absorbency rating data follow. Brand x y z 91 100 82 100 96 89 89 95 89 88 93 80 #1) At a 0.05 level of significance, does there appear to be a difference in the ability of the brands to absorb water? State the null and alternative hypotheses: A) H0: ?x ≠ ?y ≠ ?zHa: ?x = ?y = ?z B) H0: ?x = ?y = ?zHa: ?x ≠ ?y ≠ ?z C) H0: At least two of the population means are equal.Ha: At least two of the population means are different. D) H0: ?x = ?y = ?zHa: Not all the population means are equal. E) H0: Not all the population means are equal.Ha: ?x = ?y = ?z #2) Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value = #3) State your conclusion. A) Reject H0. There is…In a completely randomized experimental design, three brands of paper towels were tested for their ability to absorb water. Equal-size towels were used, with four sections of towels tested per brand. The absorbency rating data follow. Brand x y z 91 100 82 100 96 89 89 95 89 88 93 80 #1) At a 0.05 level of significance, does there appear to be a difference in the ability of the brands to absorb water? State the null and alternative hypotheses: A) H0: ?x ≠ ?y ≠ ?zHa: ?x = ?y = ?z B) H0: ?x = ?y = ?zHa: ?x ≠ ?y ≠ ?z C) H0: At least two of the population means are equal.Ha: At least two of the population means are different. D) H0: ?x = ?y = ?zHa: Not all the population means are equal. E) H0: Not all the population means are equal.Ha: ?x = ?y = ?z #2) Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value = #3) State your conclusion. A) Reject H0. There is…What are the independent and dependent variables for the following examples? What statistical test would you use for each of the following scenarios? What would you set your alpha-level at? Sally wants to examine whether there is a difference in muscular strength between participants who engaged in an 8-week resistance training program and participants who engaged in an 8-week endurance training program. The participants only took part in one of the 8-week programs, not both. What test would she use to determine whether the differences in muscular strength are significant? Why?
- In a test of H0: p = 0.4 against H1: p ≠ 0.4, a sample of size 100 produces Z = 1.28 for the value of the test statistic. Thus the p-value (or observed level of significance) of the test is approximately equal to:Suppose that you are given two random variables x and y and you take measurements and obtain x1 = 2.3%, x2 = −7.6%, x3 = 0.1% and y1 = 60, y2 = 120, y3 = 80. Find the line of best fit y = α + βx. Calculate the correlation coefficient r and perform a left-tailed hypothesis test for r with significance level 10%. Based on this test, should we use this line to find the value of y when x = .5%?x y x2 y2 xy 2.3% 60 - 120 7.6% 0.1% 80Independent random samples of 17 sophomores and 13 juniors attending a large university yield the following data on grade point averages: sophomores juniors x bar 2.84 2.75 n 17 13 s 0.52 0.31 Add the 5% significance level, does the data provide sufficient evidence to conclude that the mean GPAs of sophomores at the University are better than the juniors? 1. choose the correct parameter for the problem a. Mu1: the average GPAs of all sophomores attending a large university ; Mu2: the average GPAs of all juniors attending a large university b. All sophomores attending a large university; all juniors attending a large university c. The average GPA of all students attending a large…