Answer:
Step-by-step explanation:
To solve this problem, we'll follow the steps you've outlined:
i. Calculate the sample mean:
The sample mean of the first stream is given as 6.8, and the sample mean of the control stream is 9.2.
ii. Calculate the standard error:
The standard error can be calculated using the formula:
SE = sqrt((s1^2 / n1) + (s2^2 / n2))
where s1 and s2 are the standard deviations of the first and control streams, respectively, and n1 and n2 are the sample sizes.
For the first stream:
s1 = 2.3 (standard deviation)
n1 = 36 (sample size)
For the control stream:
s2 = 1.5 (standard deviation)
n2 = 36 (sample size)
SE = sqrt((2.3^2 / 36) + (1.5^2 / 36))
iii. Find the critical value:
Since the significance level is 0.05 and we're conducting a one-tailed test (claiming that the mean pH of the first stream is less), we need to find the critical value from the t-distribution. With a sample size of 36 - 1 = 35, the degrees of freedom (df) are 35. Using a t-table or calculator, we find the critical value for a 0.05 significance level and 35 degrees of freedom is approximately -1.692.
iv. Construct the confidence interval:
The formula for a confidence interval for the difference between two means is:
CI = (x1 - x2) ± (critical value * SE)
where x1 and x2 are the sample means.
CI = (6.8 - 9.2) ± (-1.692 * SE)
v. Interpret the confidence interval:
The confidence interval will provide a range of values within which we can be 90% confident that the true difference between the means of the first and control streams lies. Specifically, we are constructing a 90% confidence interval for the difference between the mean pH levels of the two streams.