(1) A consumer products company is formulating a new shampoo and is interested i

Question

(1) A consumer products company is formulating a new shampoo and is interested in foam height (in millimeters). Foam height is approximately normally distributed and has a standard deviation of 20 millimeters. The company wished to test H0: = 175 against H1: > 175 millimeters, using the results of n =10 samples.

(2) The life in hours of a battery is known to be approximately normally distributed, with standard deviation = 1.25. A random sample of 10 batteries has a mean life of xbar = 40.5 hours.

(A) Is there evidence to support the claim that battery life exceeds 40 hours? Use = 0.030.   

(B) What is the P-value for the test in part (a)?   

Explanation / Answer

2)

stdev = 1.25

n=10

xbar = 40.5 hours

A)

Let Ho be : X <= 40 hours

Ha : X >40 hours

X>40, alpha = .03

Z = 40.5-40/ (1.25/sqrt(10)) = +1.265

For alpha =.03 we have Z value of 1.78.

Since critical Z value is more than 1.265 , out test Z value we can't reject null hypothesis a.k.a the mean life is 40 hours.

B) P value for Z= 1.265 is 1-,8962 = .1038

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