Question

Chi square Daphne likes to ski at a resort that is open from December through April. According to a sign at the resort, 20, percent of the snow falls occur in December, 25, percent in January, 20, percent in February, 20, percent in March, and 15, percent in April. She wondered if the snow falls in her hometown followed this distribution, so she took a random sample of 80 days between December and April with snowfall and recorded their months. Here are her results:_________.

Answer 1

There is not enough evidence to suggest that the snow falls in Daphne's hometown does not follow the given distribution.

Explanation:

The missing data for the random sample of 80 days between December and April with snowfall is:

Month Days

December 16

January 11

February 16

March 18

April 19

The Chi-square goodness of fit test would be used to determine whether the snow falls in Daphne's hometown followed the given distribution.

The hypothesis for the test can be defined as follows:

H₀: The snow falls in Daphne's hometown does not follow the given distribution.

Hₐ: The snow falls in Daphne's hometown followed the given distribution.

Assume that the significance level of the test is, α = 0.05.

The Chi-square test statistic is given by:

`\chi^(2)=\sum\limits^(n)_(i=1){((O_(i)-E_(i))^(2))/(E_(i))}`

The value of Chi-square test statistic is computed in the Excel sheet below.

`\chi^(2)=\sum\limits^(n)_(i=1){((O_(i)-E_(i))^(2))/(E_(i))}=8.383`

Compute the p-value as follows:

`\text{p-value}=P(\chi^(2)_((4))>8.383)=CHISQ.DIST.RT(8.383,4)=0.0785`

The p-value of the test is 0.0785.

Decision rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected.

p-value = 0.0785 > α = 0.05.

The null hypothesis will not be rejected.

Conclusion:

There is not enough evidence to suggest that the snow falls in Daphne's hometown does not follow the given distribution.