Problem 3. [5 pts] Hypothesis Test-Single Mean A mixture of fuel ash and cement

Question

Problem 3. [5 pts] Hypothesis Test-Single Mean A mixture of fuel ash and cement is used for sealing and should have a certain minimum compressive strength. The mixture will not be used unless experimental evidence indicates conclusively that the strength specification has been met. The compressive strength for the specimens of this mixture can be assumed to be normally distributed with -60. Twenty random samples yielded an average strength of x = 1331.26 kN/m2. Test the null Hypothesis -1300 against the alternate that 1300. At what significant level would you accept the null hypothesis?

Explanation / Answer

Given that random variable X : Compressive Strength of specimen mixture follows N(, 602)

To test the hypothesis H0: = 1300 Vs H1: > 1300, we will use small sample t test as n=20.

Test statistic is,

T cal = (Sample Mean – Hypothecated Mean)*n/s ~ T (n-1)

T cal = (1331.26 – 1330)*20/60 =

The TRUE LOS will be P[ T > 0.093915 ] = 0.46308

Hence we will accept The null hypothesis at 0.46 % LOS.

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