Question

1. The proportion of defective items in a large lot of items is p. To test the hypothesis , we take a random sample of 8 items

and accept the hypothesis if the number of defectives in the sample is 6 or less. Find the probability of Type-I error of the test.

What is the Type-II error if ? What is the power of the test if ?

2. A company claims that its light bulbs are superior to those of a competitor on the basis of a study which shows that a sample of 40

of its bulbs had an average life time of 628 hours of continuous use with a s.d. of 27 hours, while a sample of 30 bulbs made by the

competitor had an average life time of 619 hours of continuous use with a s.d. of 25 hours. Check at the 5% level of significance,

whether this claim is justified. Given ( ) .

3. A die was thrown 120 times and the frequency of different faces were observed to be the following:

Face 1 2 3 4 5 6

Observed frequency 25 17 15 23 24 16

Test the hypothesis that the die is fair using a significance level of 0.05.

[Given (

) for 5 degrees of freedom].​

Answer 1

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