The tensile strengths of two materials A and B are being tested. The test is con

Question

The tensile strengths of two materials A and B are being tested. The test is conducted 10 times with following results. Material A SI 212 229 224 219 220 225 230 215 212 216 Material B (psi) 205 218 213 211 217 218 226 211 205 207 Test 1 3 4 5 8 9 10 Is there any evidence to suggest that the mean tensile strength of material A is at least 10 psi greater than that of material B? Test the hypothesis at -0.0|Use P-value method. d. Use Confidence Interval e. Clearly write your conclusion. f. If the true difference is 15 psi, what is the probability that we can detect it? g. Test the above hypothesis using 99% CI by treating both samples separately (use two samples. variance unknown, -22 scenario)

Explanation / Answer

We have given that two datasets as material A and material B.

Given that dataset of 10 observations.

Here we have to test the hypothesis that,

H0 : mu1 - mu >= 10 Vs H1 : mu < 10

where mu is population mean difference between two samples.

Here sample data is given and sample size is too small and population standard deviation is unknown so we use two sample t-test.

Assume alpha = level of significance =0.01

We can do two sample t-test in XL-stats.

Steps :

ENTER data into XL sheet --> XLSTAT -->Parametric tests --> two sample t-test ans z-test --> sample 1 : select material A data --> Sample 2 : Select material B data --> Data format : one column per sample --> Column labels --> Tests : Student's t test --> Options --> Alternative hypothesis : select less than --> Hypothesized difference : 10 --> Significance level : 1 --> Asymptotic p-value --> Assume equality --> ok

Test statistic (t) = -0.97

P-value = 0.172

P-value > alpha

Accept H0 at 1% level of significance.

COnclusion : The difference between material A and material B is atleast 10 psi.

99% confidence interval for difference between mean is (-5.883, 14.702).

Here difference is = 7.1 which is lie in the confidence interval.

Therefore accept H0 at 1% level of significance.

In the next part true difference = 15 psi which is not lie in the confidence interval so reject the null hypothesis.

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