A consumer products company is formulating a new shampoo and is interested in fo

Question

A consumer products company is formulating a new shampoo and is interested in foam height (in mm). Foam height is approximately normally distributed and has a standard deviation of 20 mm. The company wishes to test H0: = 175 mm versus H1: > 175 mm, using a random sample of n = 10 samples.

(a) Find P-value if the sample average is = 185?

(b) What is the probability of type II error if the true mean foam height is 200 mm and we assume that = 0.05? What is the power of the test?

c)If the sample size is increased to n=16. Where would the boundary of the critical region be placed if the type I error probability is 0.05?

Explanation / Answer

std error=std deviation/(n)1/2=6.325

a) here test stat z=(X-mean)/std error=(185-175)/6.325=1.58

for above p value =0.0569

b) value at 0.05 level; z=1.64485

ehnce critical value =175+1.64485*6.325=185.403

probabilty of type 2 error =P(Z<(185.403-200)/6.325)=0.0105

power of the test =1-0.0105=0.9895

c) for sample size 16; std error =5

and for 0.05 z=1.64485

hence boundary mean +z*std error =181.58

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