Factorize 4x2+9y2+16z2+12xy-24yz-16xz
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Answer:
Critical value: T = 1.8331
The 90% confidence interval for the population mean iron concentration is between 0.561 cc/m³ and 0.861 cc/m³
Step-by-step explanation:
We have the standard deviation for the sample. So we use the t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 10 - 1 = 9
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 9 degrees of freedom(y-axis) and a confidence level of . So we have T = 1.8331, which is the critical value.
The margin of error is:
M = T*s = 1.8331*0.0816 = 0.15
In which s is the standard deviation of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 0.711 - 0.15 = 0.561 cc/m³
The upper end of the interval is the sample mean added to M. So it is 0.711 + 0.15 = 0.861 cc/m³
The 90% confidence interval for the population mean iron concentration is between 0.561 cc/m³ and 0.861 cc/m³