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A study of cats and dogs found that 30 of 60 cats and 11 of 40 dogs slept more t

ID: 3357442 • Letter: A

Question

A study of cats and dogs found that 30 of 60 cats and 11 of 40 dogs slept more than 10 hours per day. At the level of significance, is there sufficient evidence to conclude that a difference exists between the proportions of cats and dogs that sleep more than 10 hours per day?

A)Yes, because the test value 7.07 is outside the noncritical region -1.96 < z < 1.96.

B)Yes, because the test value 2.24 is outside the noncritical region -1.96 < z < 1.96.

C)Yes, because the test value 5.78 is outside the noncritical region -1.65 < z < 1.65.

D)Yes, because the test value 2.66 is outside the noncritical region -1.65 < z < 1.65.

Explanation / Answer

The statistical software output for this problem is:

Two sample proportion summary hypothesis test:
p1 : proportion of successes for population 1
p2 : proportion of successes for population 2
p1 - p2 : Difference in proportions
H0 : p1 - p2 = 0
HA : p1 - p2 0

Hypothesis test results:

Hence,

Option B is correct.

Difference Count1 Total1 Count2 Total2 Sample Diff. Std. Err. Z-Stat P-value p1 - p2 30 60 11 40 0.225 0.10039505 2.2411463 0.025