Thanks! Suppose that two brands of gasoline were being compared for mlleage. Sam

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Thanks!

Suppose that two brands of gasoline were being compared for mlleage. Samples of each brand were used in Identical cars under identical conditions. Nine tests were made of Brand I and six tests of Brand II. Brand I Brand II 16 13 18 15 15 11 23 17 17 12 14 13 19 21 16 Answer the following questions using information from your assigned research problem 1. Write null and alternative hypotheses (in words and notation) appropriate for this research scenario 2. Calculate the mean, median, mode, variance and standard deviation for each column of data. 3. Compute an independent samples t-test to test the hypotheses, use an a .05, two- talled. Clearly describe the Independent and dependent variables. How do you identify M and M2? 4. Write a results paragraph that interprets and explains the results of your test 5. Compute the r2 and interpret it. What might be variables that would influence balance and walking efficiency among elderly persons, other than music-based physical training? Based on the results of the r2, frame a follow-on research problem.

Explanation / Answer

Here we have to test the hypothesis that,

H0 : mu1 = mu2 Vs H1 : mu1 not= mu2

where mu1 and mu2 are two population means.

Assume alpha = level of significance = 0.05

Sample size for brand 1 = 9

Sample size for brand 2 = 6

Two sample sizes are differ.

We will use two sample t-test assuming equal variances.

We can do two sample t-test in MINITAB.

steps :

ENTER data into MINITAB sheet --> Stat --> Basic statistics --> Two-sample t for the mean --> Each sample is in its own column --> Sample 1 : brand1 --> Sample 2 : brand2 --> Options --> Confidence level : 95.0 --> Hypothesized difference : 0.0 --> Alternative hypothesis : not= --> Assume equal variances --> ok --> ok

————— 19-06-2018 05:42:32 ————————————————————

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Two-Sample T-Test and CI: brand1, brand2

Two-sample T for brand1 vs brand2

N Mean StDev SE Mean
brand1 9 17.67 2.92 0.97
brand2 6 13.50 2.17 0.89

Difference = ? (brand1) - ? (brand2)
Estimate for difference: 4.17
95% CI for difference: (1.15, 7.19)
T-Test of difference = 0 (vs ?): T-Value = 2.98 P-Value = 0.011 DF = 13
Both use Pooled StDev = 2.6530

Test statistic = 2.98

P-value = 0.011

P-value < alpha

Reject H0 at 5% level of significance.

Conclusion : There is sufficient evidence to say that two population means differ.

brand1 Mean 17.66667 Standard Error 0.971825 Median 17 Mode 16 Standard Deviation 2.915476 Sample Variance 8.5

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