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Answer:
The 80% confidence interval for the the population mean nitrate concentration is (0.144, 0.186).
Critical value t=1.318
Step-by-step explanation:
We have to calculate a 80% confidence interval for the mean.
The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.
The sample mean is M=0.165.
The sample size is N=25.
When σ is not known, s divided by the square root of N is used as an estimate of σM:
The degrees of freedom for this sample size are:
The t-value for a 80% confidence interval and 24 degrees of freedom is t=1.318.
The margin of error (MOE) can be calculated as:
Then, the lower and upper bounds of the confidence interval are:
The 80% confidence interval for the population mean nitrate concentration is (0.144, 0.186).
Answer:
The possible rational roots are: +1, -1 ,+3, -3, +9, -9
Step-by-step explanation:
The Rational Root Theorem tells us that the possible rational roots of the polynomial are given by all possible quotients formed by factors of the constant term of the polynomial (usually listed as last when written in standard form), divided by possible factors of the polynomial's leading coefficient. And also that we need to consider both the positive and negative forms of such quotients.
So we start noticing that since the leading term of this polynomial is , the leading coefficient is "1", and therefore the list of factors for this is: +1, -1
On the other hand, the constant term of the polynomial is "9", and therefore its factors to consider are: +1, -1 ,+3, -3, +9, -9
Then the quotient of possible factors of the constant term, divided by possible factor of the leading coefficient gives us:
+1, -1 ,+3, -3, +9, -9
And therefore, this is the list of possible roots of the polynomial.