Question

On the morning of March 5, 1996, a train with 14 tankers of propane derailed near the center of the small Wisconsin town of Weyauwega. Six of the tankers were ruptured and burning when the 1700 residents were ordered to evacuate the town. Researchers study disasters like this so that effective relief efforts can be designed for future disasters. About half of the households with pets did not evacuate all of their pets. A study conducted after the derailment focused on problems associated with retrieval of the pets after the evacuation and characteristics of the pet owners. One of the scales measured "commitment to adult animals," and the people who evacuated all or some of their pets were compared with those who did not evacuate any of their pets. Higher scores indicate that the pet owner is more likely to take actions that benefit the pet. Here are the data summaries.

Group	n	x	s
Evacuated all or some pets	114	7.91	3.64
Did not evacuate any pets	122	6.27	3.51

Analyze the data and prepare a short report describing the results. (Use α = 0.01. Round your value for t to three decimal places and your P-value to four decimal places.)

t =

p - value = 0

Can you please explain in depth the steps you take to find a t statistic? thank you

Answer 1

n1 = 114

= 7.91

s1 = 3.64

n2 = 122

= 6.27

s2 = 3.51

The null and alternative hypothesis is

For doing this test first we have to check the two groups have population variances are equal or not.

Null and alternative hypothesis is

Test statistic is

F = largest sample variance / Smallest sample variances

F = 3.64^2 / 3.51^2 = 13.2496 / 12.3201 = 1.08

Degrees of freedom => n1 - 1 , n2 - 1 => 114 - 1 , 122 - 1 => 113 , 121

Critical value = 1.540

Critical value > test statistic so we fail to reject null hypothesis.

Conclusion: The population variances are equal.

So we have to use here pooled variance.

Test statistic is

Degrees of freedom = n1 + n2 - 2 = 114 + 122 - 2 = 234

Critical value = 2.597

| t | > critical value we reject null hypothesis.

Conclusion: There is sufficient evidence to support the researchers claim.