Shear strength measurements derived from unconfirmed for two types of soils gave
ID: 3220309 • Letter: S
Question
Shear strength measurements derived from unconfirmed for two types of soils gave the results shown in the following table (measurements in tons per square foot). Researches want to know the appear to differ with respect to average shear strength, at the 15% significance level? (a) Is this matched pole or two sample? (b) Write the soil and alternative hypothesis for the above claim. (d) Based on the interval, should the null hypothesis be rejected or not rejected? Why? (e) Calculate the statistics for the hypothesis test. (f) Locate the two critical values that bracket t. What are the P-values for these two entries? (g) Based on the test statistics and p-value, should the null hypothesis be rejected of not rejected? (h) Is the above t value statistically significant at the 10%level?Explanation / Answer
Answer to part a)
We make use of a 2 independent sample T test to compare the means of these two groups
.
Answer to part b)
The null hypothesis is :
Mean of both groups is same
The alternate hypothesis is :
Mean of both groups is different
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Answer to part c)
Given: n1 = 30. , n2 = 35 , x1 bar = 1.65 , x2 bar = 1.43 , s1 = 0.26 , s2 = 0.22
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The formula of confidence interval is :
(x1bar - x2bar) - t*SE , (x1bar + x2bar) + t*SE
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Formula of SE is:
SE = square root of [s1^2/n1 + s2^2/n2]
SE = square root of [0.26^2 / 30 + 0.22^2 / 35]
SE = 0.0603
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t value for df =30+35 -2 = 63 , two tailed test , alpha = 0.01
T value = 2.6561
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On plugging the value we get:
(1.65 - 1.43) - 2.6561 * 0.0603 , (1.65 - 1.43) + 2.6561 * 0.0603
0.059837 , 0.380163
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Answer to part d)
As per the null hypothesis the two groups have same mean , thus the difference of the two means must be equal to Zero
For the null hypothesis to be true, the confidence interval must include the value 0
Since the value 0 is not included in the interval 0.059837 , 0.380163 , thus we conclude that the confidence interval does not support the null hypothesis
Hence the two groups have different means
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