Question

In: Statistics and Probability

In a study of pulverized fuel-ash concrete mix, it was found that the sample mean compressive...

In a study of pulverized fuel-ash concrete mix, it was found that the sample mean compressive strength was 27.0 with a standard deviation of 4.89 for a sample of 68 specimens which had been aged for 7 days. A sample of 74 specimens which had been aged for 28 days yielded a mean compressive strength of 35.8 with standard deviation 6.43. Is there strong evidence that mean compressive strength is higher after 28 days than after 7 days? Yes, because an approximate 95% confidence interval for the difference in mean compressive strength is 8.8 ± 1.9. No, because an approximate 95% confidence interval for the difference in mean compressive strength is 8.8 ± 1.9. Yes, because an approximate 95% confidence interval for the difference in mean compressive strength is 8.8 ± 3.1. No, because an approximate 95% confidence interval for the difference in mean compressive strength is 8.8 ± 3.1. No, because a paired analysis is required for this kind of data:

Yes, because an approximate 95% confidence interval for the difference in mean compressive strength is 8.8 ± 1.9

No, because an approximate 95% confidence interval for the difference in mean compressive strength is 8.8 ± 3.1. Yes, because an approximate 95% confidence interval for the difference in mean compressive strength is 8.8 ± 3.1.

No, because an approximate 95% confidence interval for the difference in mean compressive strength is 8.8 ± 1.9.

No, because a paired analysis is required for this kind of data.

Solutions

Expert Solution

x1            = 35.80 x2            = 27.00
n1           = 74 n2           = 68
σ1           = 6.43 σ2           = 4.89
std error σx1-x2=√(σ21/n1+σ22/n2)    = 0.954
Point estimate of differnce '=x1-x2 = 8.800
for 95 % CI value of z= 1.960
margin of error E=z*std error = 1.9

correct option is:

Yes, because an approximate 95% confidence interval for the difference in mean compressive strength is 8.8 ± 1.9

(since interval values are above 0)

orchestra answered 2 years ago
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