Question

Sleep deprivation, CA vs. OR. For a recent report on sleep deprivation, the Centers for Disease Control and Prevention interviewed 11505 residents of California and 4938 residents of Oregon. In California, 920 respondents reported getting insufficient rest or sleep during each of the preceding 30 days, while 439 of the respondents from Oregon reported the same. Round each calculation to 4 decimal places.

1. Using California as population 1 and Oregon as population 2, what are the correct hypotheses for conducting a hypothesis test to determine if these data provide strong evidence the rate of sleep deprivation is different for the two states?

A. ?0:?1−?2=0H0:p1−p2=0, ??:?1−?2>0HA:p1−p2>0
B. ?0:?1−?2=0H0:p1−p2=0, ??:?1−?2<0HA:p1−p2<0
C. ?0:?1−?2=0H0:p1−p2=0, ??:?1−?2≠0HA:p1−p2≠0

2. Calculate the pooled estimate of the proportion for this test. ?̂p^ =

3. Calculate the standard error. SE =

4. Calculate the test statistic for this hypothesis test.  ? z t X^2 F  =

5. Calculate the p-value for this hypothesis test. p-value =

6. Based on the p-value, we have:
A. little evidence
B. extremely strong evidence
C. some evidence
D. very strong evidence
E. strong evidence
that the null model is not a good fit for our observed data.

Calculate the test statistic for this hypothesis test. = 5. Calculate the p-value for this hypothesis test. p-value = 6. Based on the p-value, we have: A. little evidence B. extremely strong evidence C. some evidence D. very strong evidence E. strong evidence that the null model is not a good fit for our observed data.

Answer 1

Part 1)

C. H0:p1−p2=0, HA:p1−p2≠0

p̂1 = 920 / 11505 = 0.08
p̂2 = 439 / 4938 = 0.0889

Part 2)

p̂ is the pooled estimate of the proportion P
p̂ = ( x1 + x2) / ( n1 + n2)
p̂ = ( 920 + 439 ) / ( 11505 + 4938 )
p̂ = 0.0826

Part 3)

p̂1 = 920 / 11505 = 0.08
p̂2 = 439 / 4938 = 0.0889

q̂1 = 1 - p̂1 = 0.92
q̂2 = 1 - p̂2 = 0.9111

Standard Error = = 0.0048

Part 4)

Test Statistic :-
Z = ( p̂1 - p̂2 ) / √( p̂ * q̂ * (1/n1 + 1/n2) ))
p̂ is the pooled estimate of the proportion P
p̂ = ( x1 + x2) / ( n1 + n2)
p̂ = ( 920 + 439 ) / ( 11505 + 4938 )
p̂ = 0.0826
q̂ = 1 - p̂ = 0.9174
Z = ( 0.08 - 0.0889) / √( 0.0826 * 0.9174 * (1/11505 + 1/4938) )
Z = -1.9078

Part 5)

P value = 2 * P ( Z < -1.9078 )  = 0.0564 ( From Z table )

Reject null hypothesis if P value < α = 0.05
Since P value = 0.0564 > 0.05, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

Part 6)

A. little evidence