The label on boxes of laundry detergent claims the boxes contain 39 ounces of de

Question

The label on boxes of laundry detergent claims the boxes contain 39 ounces of detergent. There is, however, some variability in the filling process. The amount of laundry detergent per box is known to follow a normal distribution. We take a random sample of 10 boxes and measure the contents. The data are as follows:

39.8 38.6 38.3 39 38 39.6 38.6 38.2 39 37.8

The sample mean and sample standard deviation are calculated to be 38.69 and 0.66, respectively.

We would like to conduct a hypothesis test to determine if there is sufficient evidence that the mean amount of detergent per box is less than 39.

Suppose we had instead used the critical value method to conduct the test. We would reject Ho if: A) t 1.372 B) It 1.383 C) t 1.833 D) t s -1.812 O E) It 1.812 F) ts -1.383 G) ts -1.833 H) t 1.812 O I) It 2 1.372 O J) t -1.372 K) t 21.383 O L) It 2 1.833

Explanation / Answer

here std errror =std deviation/(n)1/2 =0.66/(10)1/2=0.2087

value of test stat =(Xbar-mean)/std error =(38.69-39)/0.2087= -1.4854

p vlaue for above tstat at (n-1=9) degree of freedom =0.0858

as p value is less then 0.1 level of significance we reject null hypothesis that mean is equal to 39.

for 10% level of significance at 9 degree of freedom , tcritical; for Ho to be rejected t<=-1.3830

option F

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