Use the t-distribution table to find the critical value(s) for the indicated alternative hypotheses, level of significance α, and sample sizes n1 and n2. Assume that the samples are independent, normal, and random. Answer parts (a) and (b). Ha: μ1≠μ2, α=0.20, n1=18, n2= 8 (a) Find the critical value(s) assuming that the population variances are equal. (b) Find the critical value(s) assuming that the population variances are not equal.
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Use the t-distribution table to find the critical value(s) for the indicated alternative hypotheses, level of significance α, and
Ha: μ1≠μ2, α=0.20, n1=18, n2= 8
(a) Find the critical value(s) assuming that the population variances are equal.
(b) Find the critical value(s) assuming that the population variances are not equal.
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- Data on the weights (lb) of the contents of cans of diet soda versus the contents of cans of the regular version of the soda is summarized to the right. Assume that the two samples are independent simple random samples selected from normally distributedpopulations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.01 significance level for both parts. Diet Regular μ μ1 μ2 n 33 33 x 0.78488 lb 0.80356 lb s 0.00444 lb 0.00744 lb a. Test the claim that the contents of cans of diet soda have weights with a mean that is less than the mean for the regular soda. i) What are the null alternative hypothesis? ii) What's the test statics? iii) What's the P-value? iv) State the conclusion vi) construct a confidence interval suitable suitable for testing the claim that the two samples are from populations with the same mean vii) Does the confidence interval…Do a two-sample test for equality of means assuming unequal variances. Calculate the p-value using Excel. (a-1) Comparison of GPA for randomly chosen college juniors and seniors: x⎯⎯1x¯1 = 4.5, s1 = .20, n1 = 15, x⎯⎯2x¯2 = 4.9, s2 = .30, n2 = 15, α = .025, left-tailed test.(Negative values should be indicated by a minus sign. Round down your d.f. answer to the nearest whole number and other answers to 4 decimal places. Do not use "quick" rules for degrees of freedom.) d.f. Not attempted t-calculated Not attempted p-value Not attempted t-critical Not attempted (a-2) Based on the above data choose the correct decision. Do not reject the null hypothesis Reject the null hypothesisData on the weights (lb) of the contents of cans of diet soda versus the contents of cans of the regular version of the soda is summarized to the right. 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. Use a 0.05 significance level for both parts. Diet Regular mu mu 1 mu 2 n 26 26 x overbar 0.79093 lb 0.81234 lb s 0.00433 lb 0.00753 lb a. Test the claim that the contents of cans of diet soda have weights with a mean that is less than the mean for the regular soda. What are the null and alternative hypotheses? A. Upper H 0 : mu 1 equalsmu 2 Upper H 1 : mu 1 greater thanmu 2 B. Upper H 0 : mu 1 equalsmu 2 Upper H 1 : mu 1 less thanmu 2 C. Upper H 0…
- Data on the weights (Ib) of the contents of cans of diet soda versus the contents of cans of the regular version of the soda is summarized to the right. 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. Use a 0.01 significance level for both parts. Diet Regular H2 27 27 0.79037 lb 0.80399 lb 0.00449 lb 0.00756 lb a. Test the claim that the contents of cans of diet soda have weights with a mean that is less than the mean for the regular soda. What are the null and alternative hypotheses? O A. Ho: H1 = H2 OB. Ho: H1#H2 Hq: HyA random sample of n =18 data from a normal distrinution with unknown variance = 25.1 and s=3. 24. a. Find a 98% confidence interval for the population mean. b. Interpret the interval.Data on the weights (Ib) of the contents of cans of diet soda versus the contents of cans of the regular version of the soda is summarized to the right. 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. Use a 0.05 significance level for both parts. Diet Regular H2 nts 34 0.80711 lb 34 0.79119 lb 0.00432 lb 0.00747 lb 車 ent a. Test the claim that the contents of cans of diet soda have weights with a mean that is less than the mean for the regular soda. What are the null and alternative hypotheses? bra O B. Ho H1 H2 Hq: Hy < H2 O A. Ho: H1 = H2 on! O D. Hg: H1 = H2 O C. Ho H H2 The test statistic, t, is (Round to two decimal places as needed.) The P-value is |. (Round to three decimal places as needed.) State the conclusion for the test. n oonr of diet soda have mean weights that are lower than the mean weightData on the weights (lb) of the contents of cans of diet soda versus the contents of cans of the regular version of the soda is summarized to the right. 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. Use a 0.05 significance level for both parts. Diet Regular μ μ1 μ2 n 20 20 x 0.78646 lb 0.80233 lb s 0.00449 lb 0.00755 lb a. Test the claim that the contents of cans of diet soda have weights with a mean that is less than the mean for the regular soda. What are the null and alternative hypotheses? A. H0: μ1=μ2 H1: μ1≠μ2 B. H0: μ1=μ2 H1: μ1>μ2 C. H0: μ1≠μ2 H1: μ1<μ2 D. H0: μ1=μ2 H1: μ1<μ2 The test statistic, t, is nothing. (Round to two decimal places as needed.) The P-value is…A) find the critical value(s) round to 3 decimal places B) find the standard test statistic . Round to 3 decimal placesYou have data drawn from a normal distribution with a known variance of 16. You set up the following NHST: • Ho: data follows a N(2, 4²) • HÃ: data follows a N(µ, 4²) where µ ‡ 2. Test statistic: standardized sample mean z. Significance level set to a = .05. You then collected n = 16 data points with sample mean 1.5. (a) Find the rejection region. Draw a graph indicating the null distribution and the rejection region. (b) Find the z-value and add it to your picture in part (a). (c) Find the p-value for this data and decide whether or not to reject Ho in favor of HA.Find a 95% confidence interval that contains the population variance if a sample of 41 generates a sample variance of 25. Show the formula used and the quantities used and obtained from the table.Data on the weights (lb) of the contents of cans of diet soda versus the contents of cans of the regular version of the soda is summarized to the right. 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. Use a 0.05 significance level for both parts. Diet Regular μ μ1 μ2 n 26 26 x 0.78073 lb 0.80038 lb s 0.00447 lb 0.00745 lb Question content area bottom Part 1 a. Test the claim that the contents of cans of diet soda have weights with a mean that is less than the mean for the regular soda. What are the null and alternative hypotheses? A. H0: μ1=μ2 H1: μ1>μ2 B. H0: μ1=μ2 H1: μ1<μ2 Your answer is correct. C. H0: μ1≠μ2 H1: μ1<μ2 D. H0: μ1=μ2 H1: μ1≠μ2 Part 2 The test statistic, t, is…Data on the weights (Ib) of the contents of cans of diet soda versus the contents of cans of the regular version of the soda is summarized to the right. 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. Use a 0.01 significance level for both parts. Diet Regular H2 26 26 0.79911 Ib 0.81326 Ib S 0.00445 Ib 0.00759 Ib ..... a. Test the claim that the contents of cans of diet soda have weights with a mean that is less than the mean for the regular soda. What are the null and alternative hypotheses? A. Ho: Hy =H2 H1: 41> H2 B. 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