Question

. the contents of a sample of 26 cans of apple juice showed a standard deviation of 0.06 ounces. We are interested in testing to determine whether the variance of the population is significantly more than .003. At 95% confidence, what is the critical value from the table?

Answer 1

we are given

We are interested in testing to determine whether the variance of the population is significantly more than 0.003.

for this we use chi square distribution to test if the hypothetical value of the population variance is

under which the test statistic is given as:-

now for this question :

null hypothesis and alternative hypothesis is given by:

under the null hypothesis , the test statistic is:

which follows distribution with d.f.

The following information is provided:

The Chi-Square critical value for a right-tailed test, for a significance level of is:

since the calculated value of is less than the tabulated value. .

for 25 df at 5% level of significance, it is not siginificant. hence H0 may be accepted and we conclude that the data are consistent with the hypothesis. and the variance of the population is not significantly more than 0.003.

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