Question

According to Chemical Engineering an important property of fiber is its water absorbency. The average percent absorbency of 25 randomly selected pieces of cotton fiber was found to be 19.5 with a standard deviation of 1.5. A random sample of 25 pieces of acetate yielded an average percent of 12 with a standard deviation of 1.25. Is there strong evidence that the population mean percent absorbency for cotton fiber exceeds the mean for acetate by more than 7? Assume that the percent absorbency is approximately normally distributed. Use a significance level of 0.05.

(a) Write down the null and alternative hypotheses for this test.

B) what is the test statistics

(c) The p-value is:                            [ Select ]                       ["0.028", "0.007", "0.206", "0.103", "0.014"]      

(d) The appropriate decision is:

(e) What type of error may have been committed

Thank you

Answer 1

A)

The null hypothesis is given by:

H₀ : ₁ - ₂ = 7 i.e. population mean percent absorbency for cotton fiber exceeds the mean for acetate by 7.

while the alternative hypothesis is given by:

H_a : ₁ - ₂ > 7i.e. population mean percent absorbency for cotton fiber exceeds the mean for acetate by more than 7.

We are using a one tailed test

B)

Under H₀the test statistic is given by:

Here

where

N₁ = first sample size = 25

x̅₁= first sample mean = 19.5

s₁ = first sample standard deviation = 1.5

N₂ = second sample size = 25

x̅₂= second sample mean = 12

s₂ = second sample standard deviation = 1.25

Now

= 1.38067

And test statistic

= 1.2803689

C)

The P-Value is .103296

i.e Option 4

D)

Since p-value(0.103296) < 0.05, we accept the null hypothesis and conclude that population mean percent absorbency for cotton fiber exceeds the mean for acetate by 7.

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