a=0.01 n=50 p=0.02 What are the appropriate null and alternative hypotheses to t

Question

a=0.01

n=50

p=0.02

What are the appropriate null and alternative hypotheses to test?

The chi-square test statistic is 2?

The chi-square critical value is 2?

p-value?

interpret the p value.

A retailer receives shipments of batteries in packages of 50. The retailer randomly samples 400 Batteries per Package packages and tests to see if the batteries are defective. A sample of 400 packages revealed the observed frequencies shown to the right. Complete parts a and b below. Frequency of Occurrence 170 129 Number of Defective 63 30 2 4 or more

Explanation / Answer

here applying chi square test of goodness of fit:

here chi-square test statistic =9.8511

for (categories -1=5-1=4) degree of freedom and 0.01 level critical value =13.2767

p value =0.0430

which is probability of getting this or more extre mefrequency distirbution given variable follow binomial distribution with parameter n=50 and p=0.02

observed Expected Chi square defective battery Probability O E=total*p =(O-E)^2/E 0 0.364 170.000 145.67 4.06 1 0.372 129.000 148.64 2.60 2 0.186 63.000 74.32 1.72 3 0.061 30.000 24.27 1.35 4 or more 0.018 8.000 7.10 0.11 1 400 400 9.8511

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