Use the information provided to answer the questions. Population 1 Sample Size 17 13 Sample Mean 34.9 32.5 Sample Variance 4.6 5.6 LA USE SALT State the null and alternative hypotheses for testing for a significant difference in means. O Ho: (1, - 12) = 0 versus Ha: (H, - #2) 0 OH: (H, - 142) = 0 versus Ha : (1, - 12) = 0 OHp: ( 14) - 12) 0 Ho: (1 - #2) # 0 versus Ha: (#] - #2) = 0 Calculate the pooled estimate of oz, the associated degrees of freedom, and the observed value of the t statistic. (Round s and your t statistic to three decimal places.) s = 4.629 of = 28 1 = 3.028 What is the rejection region using a = 0.05? (If the test is one-tailed, enter NONE for the unused region. Round your answers to three decimal places. t > 2.048 t 0.200In a study on the effect of an oral rinse on plaque buildup on teeth, sixteen people whose teeth were thoroughly cleaned and polished were randomly assigned to two groups of eight subjects each. Both groups were assigned to use oral rinses (no brushing) for a 2-week period. Group 1 used a rinse that contained an antiplaque agent. Group 2, the control group, received a similar rinse except that the rinse contained no antiplaque agent. A measure of plaque buildup was recorded at 14 days with means and standard deviations for the two groups shown in the table. Control Group Antiplaque Group Sample Size Mear 1.22 0.77 Standard Deviation 0.33 0.33 LA USE SALT (a) State the null and alternative hypotheses that should be used to test the effectiveness of the antiplaque oral rinse. O Ho: (141 - 42) = 0 versus Ha: (141 - #2) 0 O Ho: (/41 - #2) = 0 versus Ha: (#] - #2) = 0 Ho: (141 - 42) = 0 versus Ha: (/] - #2) > 0 (b) Do the data provide sufficient evidence to indicate that the oral antiplaque rinse is effective? Test using a = 0.05. State the test statistic. (Round your answer to three decimal places.) t = 2.7273 State the rejection region. (If the test is one-tailed, enter NONE for the unused region. Round your answers to three decimal places.) t > 2.1448 -2.1448 XData on the estimated average price for a variety of different brands of tuna, based on prices paid nationally in supermarkets, are shown in the following table. Use the MINITAB printout to answer the questions in parts (a)-(c). (Use the exact values found in the MINITAB output.) Light Tuna Light Tuna in Water in oil 0.97 0.55 2.54 0.64 1 94 1.39 1.90 0.68 1.21 1.14 1.28 0.60 1.83 0.65 1.81 0.67 0.67 0.65 1.25 0.62 0.67 0.58 0.65 0.58 0.64 Two-Sample T-Test and CI: Light Water, Light oil Descriptive Statistics Sample N Mean St Dev SE Mean Light Water 14 0. 891 0. 403 0.11 Light Oil 1.149 0. 671 0.20 Estimation for Difference 958 CI for Difference Pooled StDev difference -D. 258 D. 536 -0. 705, 0.108) Test Null hypothesis Ho: H - #2 - 0 Alternative hypothesis T-Value DE P-Value -1.20 23 0.244 (a) Do the data in the table present sufficient evidence to indicate a difference in the s of light tuna in water versus oil? Test using a = 0.05. State the null and alternative hypotheses. O Ho: ( #, - (2) = 0 versus Hat (H, - H2) 0 O Ho: (141 - 12) = 0 versus Hai (1] - 12) > 0 OH: ( M, - 12 ) = 0 versus Ha : (H, - H2) 7 0 State the test statistic. t - State the rejection region. (If the test is one-tailed, enter NONE for the unused region. Round your answers to three places.) t > State the conclusion. O Ho is not rejected. There is insufficient evidence to conclude that there is a difference in the average prices of light tuna in water versus oil. O Ho is rejected. There is insufficient evidence to conclude that there is a difference in the average prices of light tuna in water versus oil. O Ho is rejected. There is sufficient evidence to conclude that there is a difference in the average prices of light tuna in water versus oil. O Ho is not rejected. There is sufficient evidence to conclude that there is a difference in the average prices of light tuna in water versus oil. (b) What is the p-value for the test? p-value = (c) The MINITAB analysis uses the pooled estimate of of. Is the assumption of equal variances reasonable? Why or why not? (Round your answer to three decimal places.) The ratio of the larger of the two sample variances to the smaller iswhich is [---Select-.- v than 3, so the assumption of equal variances ---Select--- |reasonable.To test the effect of alcohol in increasing the reaction time to respond to a given stimulus, the reaction times of seven people were measured both before and after consuming 3 ounces of 40% alcohol. Do the following data indicate that the mean reaction time after consuming alcohol was greater than the mean reaction time before consuming alcohol? Use a = 0.05. (Use "before - Hafter "Ha") Person 1 2 3 4 5 6 Before 6 5 After 9 6 3 4 LA USE SALT State the null and alternative hypotheses. O Ho: Hy # 0 versus Hai Hd = 0 O Ho: Hy = 0 versus Ha: Hy # 0 O Ho: My 0 O Ho: Hy = 0 versus Hai Hy > 0 O Ho: Hid = 0 versus Ha: Hy State the conclusion. O Ho is rejected. There is sufficient evidence to indicate that the mean reaction time is greater after consuming alcohol. O Ho is rejected. There is insufficient evidence to indicate that the mean reaction time is greater after consuming alcohol. O Ho is not rejected. There is sufficient evidence to indicate that the mean reaction time is greater after consuming alcohol. O Ho is not rejected. There is insufficient evidence to indicate that the mean reaction time is greater after consuming alcoholA survey was conducted by an independent price-checking company to check an advertiser's claim that it had lower prices than it competitors. The average weekly total, based on the prices of approximately 95 items, is given for this chain and for its competito recorded during four consecutive weeks in a particular month Week Advertiser ($) Competitor ($) 1 254.16 256.13 2 240.57 255.70 3 231.82 255.18 A 234.16 261.15 LO USE SALT (a) Is there a significant difference in the average prices for these two different supermarket chains? (Use a = 0.05. Use Hadvertiser - "competitor " Had State the null and alternative hypotheses. O Ho: My = 0 versus Hai Hy 0 Hy: My = 0 versus Hai Hy # 0 O Ho: My 0 O Ho: My # 0 versus Ha: Ha = 0 State the test statistic. (Round your answer to three decimal places.) t . -2.988 x State the rejection region. (If the test is one-tailed, enter NONE for the unused region. Round your answers to three decime places.) t > 0.05 t 0 T-Value P-Value 3.27 0:007 (a) Do the data provide sufficient evidence to indicate that assessor 1 tends to give higher assessments than assessor 2? (Use a - 0.05) State the null and alternative hypotheses. O Ho: Ly 0 O Ho: My = 0 versus Ha: Ha # 0 O Ho: My # 0 versus Ha: Ha = D O Ho: My = 0 versus Ha: Ha 0 State the test statistic. State the p-value. State the conclusion. O Ho is not rejected. There is ssments than assessor B. O Ho is rejected. There is sufficient ents than assessor B. O Ho is rejected. There is insufficient evidence to in sments than assessor B. O Ho is not rejected. There is insufficient evidence to indicate assessor A gives higher assessments than assessor B. (b) Estimate a 95% lower one-sided confidence bound. (Use #1 - #2.) (c) What assumptions must you make in order for the inferences in parts (a) and (b) to be valid? (Select all that apply.) The properties must be randomly selected. The properties must be independently selected. The assessments must be normally distributed. O The variance of the data sets for both assessors must be equal. The sample size must be greater than 5 for each assessor