5-1 Discussion: Applications of Two-Sample Tests Available after Saturday, July

Question

5-1 Discussion: Applications of Two-Sample Tests Available after Saturday, July 28, 2018 11:59 PM EDT Choose one of the following two prompts to respond to. In your two follow up posts, respond at least once to each prompt option. Use the discussion board as a place to ask questions, speculate about answers, and share insights. Be sure to embed and cite your references for any supporting images. Option 1: Think of a problem that you may be interested in that deals with a comparison of two population means. Propose either a confidence interval or a hypothesis test question that compares these two means. Gather appropriate data and post your problem (without a solution) in the discussion board. Once your initial post is complete, respond to your own post with the solution for others to check their work. Option 2:

Explanation / Answer

There are two parametric tests to compare two population means.

i) Two sample Z-test for means

ii) Two sample t-test for means

The amount of a certain trace element in blood is known to vary with a standard deviation of 14.1 ppm (parts per million) for male blood donors and 9.5 ppm for female donors. Random samples of 75 male and 50 female donors yield concentration means of 28 and 33 ppm, respectively. What is the likelihood that the population means of concentrations of the element are the same for men and women?

Here we have to test the hypothesis that,

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

where mu1 is population mean for first sample

mu2 is population mean for second sample.

Assume alpha = level of significance = 0.05

Given that,

X1bar = 28 ppm

X2bar = 33 ppm

s1 = 14.1 ppm

s2 = 9.5 ppm

n1 = 28

n2 = 20

Here sample data is given and sample sizes are < 30 so we use two sample t-test assuming equal variances.

We can do this test in MINITAB.

steps :

STAT --> Basic statistics --> Two sample t --> Summarized data --> Input all the values --> Options --> COnfidence level : 95.0 --> Hypothesized difference : 0.0 --> Alternative hypothesis : not= --> Assume equal variances --> ok --> ok

————— 02-08-2018 10:37:05 ————————————————————

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Two-Sample T-Test and CI

Sample N Mean StDev SE Mean
1 28 28.0 14.1 2.7
2 20 33.00 9.50 2.1

Difference = ? (1) - ? (2)
Estimate for difference: -5.00
95% CI for difference: (-12.31, 2.31)
T-Test of difference = 0 (vs ?): T-Value = -1.38 P-Value = 0.175 DF = 46
Both use Pooled StDev = 12.4085

Test statistic = -1.38

P-value = 0.175

P-value > alpha

Accept H0 at 5% level of significance.

COnclusion : There is sufficient evidence to say that two population means are equal.

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