Question

Another medical student named Emily is also studying the population of pregnant women in the United States, and is also interested in the duration of their pregnancies (in days). Emily will compute a 95% confidence interval. Like Sheena, Emily knows that the population standard deviation equals 16 days. Emily takes a random sample of 20 pregnant women (this is a different random sample than Sheena's!). The sample mean duration among the 20 pregnancies in Emily's sample equals 278. Emily's 95% confidence interval equals ( A, B ). What is the value of B? Round off to the second decimal place.

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Question 71 pts

Suppose Emily decided that the error margin of her 95% confidence interval was too large and wanted an error margin of 1.7 days while maintaining a 95% confidence level. She should take another random sample of size n = _________. (Remember to always round sample sizes up to the next integer.)

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Question 81 pts

If Emily had used the same data to compute a 99% confidence interval (instead of a 95% confidence interval), it would have been _________.

Group of answer choices

the same width

wider

thinner

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Question 91 pts

For both Sheena’s hypothesis test and Emily's confidence interval, what is statement is true?

Group of answer choices

Since the sample size is large, they are NOT required to assume the population is normally distributed.

Since the sample size is large, they ARE required to assume the population is normally distributed.

Since the sample size is small, they are NOT required to assume the population is normally distributed.

Since the sample size is small, they ARE required to assume the population is normally distributed.

Answer 1

Level of Significance ,    α =    0.05          
'   '   '          
z value=   z α/2=   1.9600   [Excel formula =NORMSINV(α/2) ]      
                  
Standard Error , SE = σ/√n =   16.0000   / √   20   =   3.5777
margin of error, E=Z*SE =   1.9600   *   3.5777   =   7.0122
                  
confidence interval is                   
Interval Lower Limit = x̅ - E =    278.00   -   7.012180   =   270.9878
Interval Upper Limit = x̅ + E =    278.00   -   7.012180   =   285.0122
95%   confidence interval is (   270.99   < µ <   285.01   )

so, value of B = 285.01

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Question 7

Standard Deviation ,   σ =    16                  
sampling error ,    E =   1.7                  
Confidence Level ,   CL=   95%                  
                          
alpha =   1-CL =   5%                  
Z value =    Zα/2 =    1.960   [excel formula =normsinv(α/2)]              
                          
Sample Size,n = (Z * σ / E )² = (   1.960   *   16   /   1.7   ) ² =   340.281
                          
                          
So,Sample Size needed=       341                  
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8)

If Emily had used the same data to compute a 99% confidence interval (instead of a 95% confidence interval), it would have been _________.

wider

because greater the confidence interval, greater is margin of error, wider the interval

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9) Since the sample size is small, they ARE required to assume the population is normally distributed