Question

Data Set	Average	Standard Deviation	N
A	59.4	11.01	12
B	58.4	11.86	15

USING T DISTRIBUTION AND HYPOTHESIS TESTING

For dataset A and B, what is the confidence for the true mean of each is greater than 60?

Determine if there is a significant difference between the two viscometers in measuring the fluid viscosity with 95% confidence

For meter A, if we want the uncertainty to be the same as the uncertainty in question 2, but the confidence to be at 99%, how many more measurements are needed (assume the mean and standard deviation are the same)?

Answer 1

For dataset A and B, what is the confidence for the true mean of each is greater than 60?

For A:

60.000	hypothesized value
59.400	mean A
11.010	std. dev.
3.178	std. error
12	n
11	df
-0.189	t
.5731	p-value (one-tailed, upper)

For B:

60.000	hypothesized value
58.400	mean B
11.860	std. dev.
3.062	std. error
15	n
14	df
-0.522	t
.6953	p-value (one-tailed, upper)

Determine if there is a significant difference between the two viscometers in measuring the fluid viscosity with 95% confidence

The hypothesis being tested is:

H₀: µ₁ = µ₂

H₁: µ₁ ≠ µ₂

A	B
59.4	58.4	mean
11.01	11.86	std. dev.
12	15	n
	25	df
	1.0000	difference (A - B)
	132.1062	pooled variance
	11.4937	pooled std. dev.
	4.4515	standard error of difference
	0	hypothesized difference
	0.225	t
	.8241	p-value (two-tailed)

Since the p-value (0.8241) is greater than the significance level (0.05), we cannot reject the null hypothesis.

Therefore, we cannot conclude that there is a significant difference between the two viscometers in measuring the fluid viscosity.

For meter A, if we want the uncertainty to be the same as the uncertainty in question 2, but the confidence to be at 99%, how many more measurements are needed (assume the mean and standard deviation are the same)?

9 more measurements