A metropolitan childrens museum open yearround wants to see

A metropolitan children\'s museum open year-round wants to see if the variance in daily attendance differs between the summer and winter months. Random samples of 30 days each were selected and showed that in the winter months, the sample mean daily attendance was 300 with a standard deviation of 52, and the sample mean daily attendance for the summer months was 280 with a standard deviation of 65. At = 0.05, can we conclude a difference in the variances?

Step 1: State hypotheses by filling in the symbol (=, <, >, or not equal):

H_o: ₁

H₁: ₁

Step 2: Find the critical value (from the table) (example: 2.34)

Critical F value is:

Step 3: Compute the test value using the formula (round to two decimal places, example 6.45, and it is always greater than 1):

F test value is:

Step 4: Reject the null or do not reject the null (type in either Reject the null or do not reject the null only):

Step 5: Conclusion sentence (type in either is or is not only, to reflect what you found):

There      enough evidence to support the claim that the variances in daily attendance differs between the summer and winter months.

Solution

Null Hypothesis, There Is No Significance between them Ho: ^2 = ^2
Alternate Hypothesis, There Is Significance between them H1: ^2 != ^2
Test Statistic
Sample 1
s1^2=4225, n1 =30
Sample 2
s2^2 =2704, n2 =30
Fo =4225/2704 = 1.56
| Fo | =1.56
Critical Value
The Value of |F | at LOS 0.05 with d.f F(n1-1,n2-1)=F(29,29) is 2.101
We got |Fo| =1.563 & | F | =2.101
Make Decision
Hence Value of |Fo | < | F | and Here we Do not Reject Ho

There is n\'t enough evidence to support the claim that the variances in daily attendance differs between the summer and winter months