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3. The table to the right shows the cost per ounce (in dollars) for a random sample of toothpastes exhibiting very good stain removal, goad stain removal, and fair stain removal. At α= 0.01, can you conclude that the mean costs per ounce are different? Perform a one-way ANOVA test by completing parts a through d. Assume that each sample is drawn from a normal population, that the samples are independent of each other, and that the populations have the same variances. ry good stain stain stain 0.35 0.37 2.79 1.28 0.48 0.46 0.60 1.58 0.42 0.64 0.75 0.33 1.32 64 34 (a) Identfy the claim and state Ho and Ha. Choose the correct answer below. A B. HO : At least one HO : μ1-μ2-μ3 Ha: At least one mean is different from the others. (claim) mean is different from the others. claim) (claim) Ha: At least one mean is different from the others. H: At least two means are different from the others. claim) (b) Identify the degrees of freedom for the numerator and for the denominator, determine the critical value, and determine the rejection region. The degrees of freedom for the numerator, d.f.N. is The critical value is Fo (Round to two decimal places as needed.) The rejection region is F (1) (Round to two decimal places as needed.) (c) Calculate the test statistic. and the degrees of freedom for the denominator, d.f.D, is (Round to three decimal places as needed.) (d) Decide to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim. Choose the correct decision below. A Since F is in the rejection region, fail to reject Ho B. Since F is in the rejection region, reject Ho -, C. Since F is not in the rejection region, fail to reject Ho D. Since F is not in the rejection region, reject Ho Choose the correct interpretation below. There (2) enough evidence at the 1% significance level to (3)--the claim that the mean cost per ounce is (4) (1) > に2)-) is not (3)-, support (4) the same for all three products is disputedifferent for at least one product4. Assume the samples are random and independent, the populations are normally distributed, and the population variances are equal. The table available below shows the prices (in dollars) for a sample of automobile battenes. The prices are classified according to battery type. At α = 0.01, is there enough evidence to conclude that at least one mean battery price is different from the others? Complete parts (a) through (e) below. Click the icon to view the battery cost data. a) Let μ1 μ2+3 represent the mean prices for the group size 35.65, and 24/24F respectively. Identify the claim and state Ho and Ha Ha: (2)_ The claim is the (3)-hypothesis. (b) Find the critical value, Fo. and identfy the rejection region. The rejection region is F(4)_Fowhere Fo (Round to two decimal places as needed.) (c) Find the test statistic F Round to two decimal places as needed.) (d) Decide whether to reject or fail to reject the null hypothesis. (5)Ho because the test statistic (6) (e) Interpret the decision in the context of the original claim. There (7)enough evidence at the in the rejection region. % level of significance to (8)--the claim that (9) mean battery price is(10)--the others. Type an integer or a decimal.) 1: Cost of batteries Group size 35 size 65 sze 24/24F (1), None of the means are equal-ri μ2 μ3 (2) -. At least one mean is different from the others. s μ2-μ3, μ1 # μ2 (9} -alternative (4) At least one mean is different from the others H2 H3 null e None of the means are equal. (5) Reject 6is notis not (8) support(9at least one 10different from reject Fail to reject is all but one the same as5. The table available below shows the weights (in pounds) for a sample of vacuum cleaners. The weights are classified according to vacuum cleaner type. At α = 0.10, can you conclude that at ast one mean vacuum cleaner weight is different from the others? Click the icon to view the vacuum cleaner weight data. Let μ U BLU and HTC represent he mean weights for bagged upnght, bagless upright, and top canister vacuums respectively. What are the hypotheses for this test? A. Ho: At least one of the means is different. H: At least one of the means is different. What is the test statistic? Round to two decimal places as needed.) What is the P-value? P-value- What is the correct conclusion? Round to three decimal places as needed.) A. Do not reject Ho. There is not enough evidence to conclude that mean weights vary across the vacuum cleaner types. B. Reject Ho. There is not enough evidence to conclude that mean weights vary across the vacuum cleaner types. -C. Reject HO. There is enough evidence to conclude that mean weights vary across the vacuum cleaner types. D. Do not reject Ho. There is enough evidence to conclude that mean weights vary across the vacuum cleaner types. 2: of Vacuum Cleaners Top anister6. e table available below shows the costs per mile (in cents) for a sample of automobiles. At α= 0.01, can you conclude that at least one mean cost per mile is different from the others? Click on the icon to view the data table. LetụSS MS,pLS μSUV and μΜν represent the mean costs per mile for small sedans, medium sedans, la this test? e sedans SUV 4 Ds, and min ans respecti ely. what are e hypotheses or Ha: Not all the means are equal. B. Ho: Not all the means are equal. What is the test statistic? STAT = What is the P-value? P-value- What is the correct conclusion? (1)Ho. There (2) 3: Advertising Scores Round to two decimal places as needed.) Round to three decimal places as needed.) enough evidence to conclude that mean costs per mile vary across the automobile types. Small Medium Large SUV Minivan sedan sedan sedan 4WD 59 74 160 54 60 62 53 50 6 64 68 67 68 68 64 54 64 59 62 (1) Reject (2) is Do not reject snot7. The data found below measure the amounts of greenhouse gas emissions from three types of vehicles. The measurements are in tons per year, expressed as CO2 equivalents. Use a 0.05 significance level to test the claim that the different types of vehicle have the same mean amount of greenhouse gas emissions. Based on the results, does the type of vehicle appear to affect he amount of greenhouse gas emissions? Click the icon to view the data. What are the hypotheses for this test? H.: At least one of the means is different from the others. C. Ho: At least one of the means is different from the others. Determine the test statistic. Round to two decimal places as needed.) Identify the P-value. P-value- What is the conclusion of the test? (1) the null hypothesis. Conclude that the type of vehicle (2)appear to affect the amount of greenhouse gas emissions for these three types. 4: Data Table Round to two decimal places as needed.) Type Type 5.9 6.7 5.6 6.4 6.8 5.6 6.3 5.9 6.9 6.1 5.8 5.8 6.87.2 6.4 5.6 6.8 5.6 5.75.76.6 7.1 6.3 5.7 6.3 7.4 (1) Reject 2)does not Do not reject does

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Answer #1

(1)

(a) Option A

One factor ANOVA Mean n Std. Dev 0.625 6 0.4819 Very good 1.063 6 0.9058 Good 0.740 3 0.4854 Fair 0.823 15 0.6728 Total ANOVA table Source df MS Treatment 0.6025 2 0.30123 Error Total 0.63 5492 5.7347 12 0.47789 6.3371 14

(b) dfN = 2, dfD = 12, Critical F = 6.93

The rejection region is F > 6.93

(c) F = 0.630

(d) Option C

(e) Not, reject, Equal

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