Hypothesis Testing: numbers of words spoken by each member of 6 randomly selected...

[noahpww]

Listed below are the numbers of words spoken in a day by each member of six randomly selected couples:

Male: 5638, 21319, 17572, 26429, 46978, 25835
Female: 5198, 11661, 19624, 13397, 31553, 18667

Use a 0.05 significance level to test the claim among couples, males speak more words in a day than females.

(a) State the original claim and the opposite in symbolic form:


(b) State the null hypothesis H₀, the alternative hypothesis H₁, and the type of test:


(c) State the testing method and the test you used, and relevant formulas/values:


(d) State the relevant test result(s) and the associated rejection criterion:


(e) State your conclusions:
A. There is sufficient evidence to support the claim.
B. There is not sufficient evidence to support the claim.
C. There is sufficient evidence to reject the claim.
D. There is not sufficient evidence to reject the claim.

Any help with this would be greatly appreciated!

 

[HallsofIvy]

What do you understand about this problem? For example, do you know what "state the original claim and the opposite in symbolic form" means?

 

[noahpww]

Would the original claim = p > 0.05 and the opposite = p (less than or greater) to 0.05?

 

[Agent Smith]

Is this correct?
I don't see any mention of the normality of both distributions (male & female). Are we supposed to assume this? The sample size for each group < 30 (there are only 6 males and 6 females).

 

[mario99]

View attachment 38847
View attachment 38848
Is this correct?
I don't see any mention of the normality of both distributions (male & female). Are we supposed to assume this? The sample size for each group < 30 (there are only 6 males and 6 females).

Rule of Thumb: If the sample is small and related (couples), the correct way is to use the T-test, not the Z-test.

 

[Agent Smith]

Rule of Thumb: If the sample is small and related (couples), the correct way is to use the T-test, not the Z-test.

Thanks. Yes, the sample is small. For degree of freedom do we use the smaller sample size between the two? In this case both samples are size 6. So I should use 6 - 1 = 5 as the degree of freedom, correct?

Are there different types of t tables or only 1 that works for all calls for a t table?



Otherwise ... all ok?

 

[mario99]

Thanks. Yes, the sample is small. For degree of freedom do we use the smaller sample size between the two? In this case both samples are size 6. So I should use 6 - 1 = 5 as the degree of freedom, correct?

Yes.

Are there different types of t tables or only 1 that works for all calls for a t table?

Otherwise ... all ok?

There are two T-tables: one tail and two tails. The context of this problem is suitable for one tail.