Question

Use me Tonowing steps to calculate we yo comuncu Merval Tor me uuerence II mean temperature between the two rivers. a) What is the estimate for the standard error of the difference between the two means? giv b) i Using degrees of freedom, v = 41.92, what is the appropriate multiplier to use for this calculation? Calculate the 95% confidence interval for the difference in mean temperature in the affected and unaffected rivers (uaffected - Munaffected). (i) The lower limit of the confidence interval is: giv gi (ii) The upper limit of the confidence interval is: d) From your answers in c) select the appropriate conclusion to your confidence interval: We are 95% confident that the difference in mean temperature between the two rivers lies within the limits found above, as zero is excluded from the confidence interval there is no evidence of a difference in mean temperature between the two rivers. We are 95% confident that the difference in mean temperature between the two rivers lies within the limits found above, as zero is included in the confidence interval there is evidence of a difference in mean temperature between the two rivers. We are 95% confident that the true mean temperature between the two rivers lies within the limits found above, as zero is excluded from the confidence interval, and the interval is entirely positive, there is evidence that mean temperature is higher in the affected river than the unaffected river. We are 95% confident that the true mean difference in temperature between the two rivers lies within the limits found above, as zero is included in the confidence interval there is no evidence of a difference in mean temperature between the two rivers. We are 95% confident that the true mean temperature between the two rivers lies within the limits found above, as zero is excluded from the confidence interval, and the interval is entirely negative, there is evidence that mean temperature is lower in the affected river than the unaffected river. e) Imagine the researchers would like to be able to estimate the mean difference in river temperature to within 0.6 degrees Celsius. Find the minimum number of readings that should be taken from each river in order to achieve a margin of error for the difference between the mean river temperatures to be at most 0.6 degrees Celsius. Assume that the same number of measurements is taken from each river. Remember to round your answer up to the nearest integer.

Answer 1

a.

The estimate for the standard error of the difference between the two means is 0.02 (0.44 - 0.42)

Two-Sample T-Test and CI

Method

μ₁: mean of Sample 1

µ₂: mean of Sample 2

Difference: μ₁ - µ₂

Equal variances are not assumed for this analysis.

Descriptive Statistics

Sample	N	Mean	StDev	SE Mean
Sample 1	23	16.52	2.10	0.44
Sample 2	21	15.40	1.90	0.42

Estimation for Difference

Difference	95% CI for Difference
1.120	(-0.100, 2.340)

Test

Null hypothesis	H₀: μ₁ - µ₂ = 0
Alternative hypothesis	H₁: μ₁ - µ₂ ≠ 0

T-Value	DF	P-Value
1.85	41	0.071

b.)

The appropirate multiplier to use for calculation is 1.85 (t-statistic value)

c)

Confidence Interval

Lower limit = -0.1000

Upper limit = 2.340

d)

The p-value =0.071 and alpha value =0.05 for 95% of confidence interval

The p-value is greater than alpha value then Accept Ho (null hypothesis)

Conclusion: There is no significance difference between affected river and unaffected river at 5% of level of significance.

We are 95% confident that true mean difference in temperature between the two rivers lies within the limits found above,as zero is included in the confidence interval there is no evidence of a difference in mean temperature between the two years.