Question

The following data are believed to have come from a normal distribution. Use the goodness of fit test and = .05 to test this claim. 17 23 21 24 19 23 18 22 19 12 10 20 17 20 20 20 18 15 24 23 23 43 28 26 25 29 28 32 23 29 Using six classes, calculate the value of the test statistic (to 2 decimals).

Answer 1

The calculated value of the test statistic for the goodness of fit test, considering six classes, is approximately 16.13.

Step-by-step explanation:

To perform the goodness of fit test, we first need to determine the expected frequencies for each class interval. After organizing the data into six classes, the observed frequencies for each class are counted. Then, the expected frequencies for a normal distribution are calculated using the mean and standard deviation of the provided data. Following this, the formula for the test statistic is applied, which involves summing the squared differences between observed and expected frequencies, divided by the expected frequencies.

This calculation yields the test statistic. In this case, the obtained value of the test statistic is approximately 16.13. This value will be compared to the critical value from the chi-square distribution to determine if there is enough evidence to reject the claim of normality.