Question

 

For each problem, perform the following steps. Assume that all variables are normally or approximately normally distributed.

1. State the hypothesis and identify the claim.

2. Find the critical value(s).

3. Compute the test value.

4. Make the decision.

5. Summarize the results.

5. The heights (in feet) for a random sample of world famous cathedrals are listed below. In addition, the heights for a sample of the tallest buildings in the world are listed. Is there sufficient evidence at α = 0.05 to conclude that there is a difference in the variances in height between the two groups? [4]

Cathedrals	72	114	157	56	83	108	90	151
Tallest buildings	452	442	415	391	355	344	310	302	209

Answer 1

The sample size is n = 8 . The provided sample data along with the data required to compute the sample variance are shown in the table below:

	X	X2
	72	5184
	114	12996
	157	24649
	56	3136
	83	6889
	108	11664
	90	8100
	151	22801
Sum =	831	95419

Also, the sample variance  

The sample size is n = 9 The provided sample data along with the data required to compute the sample variance are shown in the table below:

	X	X2
	452	204304
	442	195364
	415	172225
	391	152881
	355	126025
	344	118336
	310	96100
	302	91204
	209	43681
Sum =	3220	1200120

Also, the sample variance  

Null hypothesis: Variance are equal

H0:

Alternate hypothesis: Variance are unequal

Ha:

df_1 = n_1- 1 = 8 - 1 = 7

df_2 = n_2 - 1 = 9 - 1 = 8

F_critical_L = 0.204

F_critical_U = 4.529

Reject null hypothesis , if F < F_L and F > F_U

Since, F > F_L critical Null hypothesis is not rejected.

hence, 2 variances are equal