If we decided to use the normal distribution instead of the t distribution to ma
ID: 3181045 • Letter: I
Question
If we decided to use the normal distribution instead of the t distribution to make our 95% confidence intervals they would be more narrow, but when n is large the difference between the t and normal distributions is minor. If comparing the width of the 95% confidence intervals calculated in these two ways, the interval based on the normal distribution is roughly __% as wide as that using the t distribution for n=100. (provide the closest value) 95.0% 97.5% 98.0% 98.5% 98.8% If we decided to use the normal distribution instead of the t distribution to make our 95% confidence intervals they would be more narrow and when n is small the difference between the t and normal distributions can be large. If comparing the width of the 95% confidence intervals calculated in these two ways, the interval based on the normal distribution is roughly __% as wide as that using the t distribution for n=20. (provide the closest value) 94% 95% 96% 97% 98%Explanation / Answer
when n is small ( less than 30)
(1-alpha)*100% confidence interval for population mean=mean±t(alpha/2,n-1)*sd/sqrt(n)
95% confidence interval for population mean=mean±t(0.05/2, n-1)*sd/sqrt(n)
when n is large(more than 30)
(1-alpha)*100% confidence interval for mean=mean± z(alpha/2)*sd/sqrt(n)
95% confidence interval for mean=mean±z(0.05/2)*sd/sqrt(n)
(7) required answer is (A)95%
the z-value used for calculating 95% confidence interval =z(0.05/2)=1.96 ( here alpha=0.05)
the corresponding alpha using t-value 1.96 is .0.0528 (using ms-excel command==TDIST(1.96,99,2) and confidence %=0.9472
(8) required answer is (A)94%
the z-value used for calculating 95% confidence interval =z(0.05/2)=1.96 ( here alpha=0.05)
the corresponding alpha using t-value 1.96 is .0.0648 (using ms-excel command=TDIST(1.96,19,2) and
confidence %=0.9352
the two decimal approximation=0.94 and required answer is (A)94%
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