Question

A distribution and the observed frequencies of the values of a variable from a simple random sample of the population are provided below. Use the chi-square goodness-of-fit test to decide, at the specified significance level, whether the distribution of the variable differs from the given distribution Distribution: 0.1875, 0.1875, Observed frequencies: 16, 20, 24, 36 Significance level 0.05 0.3125, 0.3125 Determine the null and alternative hypotheses. Choose the correct answer below. OA. H: The distribution of the variable differs from the given distribution B. Ho: The distribution of the variable is the same as the given distribution. O C. Ho: The expected frequencies are all equal to 5. Ha: The distribution of the variable is the same as the given distribution. Ha: The distribution of the variable difers from the given distribution Ha: At least one expected frequency differs from 5. D. Ho: The distribution of the variable differs from the normal distribution. На: H: The distribution of the variable is the normal distribution Compute the value of the test statistic, z Find the P-value. Choose the correct answer below. OA. 0.05

Answer 1

The Hypotheses are:

Ho: The distribution of the given variable is same as the given distribution

Ha: The distribution of the variable is different from the given distribution

The Chi-square value is calculated using the tabulated form as

Diff. Sq. /Exp Fr Expected 18 18 30 30 Difference Sq. 16 2.00 2.00 8.00 8.00 4.00 4.00 38.00 38.00 0.22 0.22 1.20 1.20 20 36 2.844

The Chi-square value is 2.844

and the P-value associated with chi-square value is

E. P>0.1

Conclusion:

No, because there is not sufficient evidence to reject the null hypothesis.

P-value computed using the Chi-square table shown below as

10 (r-16 11 84 64 04 33 90 68 00 r 04 03 2 1 45 00001 12233 02000000 1122 0 250 122 0 r12345 67890