Question

2) A random sample of 10 miniature Tootsie Rolls was taken from a bag. Each piece was weighed on a very accurate scale. The results in grams were:

3.087 3.131 3.241 3.241 3.270 3.353 3.400 3.411 3.437 3.477

-Assuming a normal population, use Minitab to construct a 95 percent confidence interval for the true mean weight. You will need to enter the data. Attach or include your output. (4 points)

-Write a sentence using the confidence interval found in part a. (3 points)

-Use Minitab to construct a histogram of the sample data. Use the histogram to determine if the

assumption of normality is a valid assumption. State your findings. (4 points)

-What sample size would be necessary to estimate the true weight with an error of ± 0.025 gram

with 90 percent confidence? (4 points)

Answer 1

MINITAB used.

2) A random sample of 10 miniature Tootsie Rolls was taken from a bag. Each piece was weighed on a very accurate scale. The results in grams were:

3.087 3.131 3.241 3.241 3.270 3.353 3.400 3.411 3.437 3.477

-Assuming a normal population, use Minitab to construct a 95 percent confidence interval for the true mean weight. You will need to enter the data. Attach or include your output. (4 points)

One-Sample T: weight

Descriptive Statistics

N	Mean	StDev	SE Mean	95% CI for μ
10	3.3048	0.1320	0.0417	(3.2104, 3.3992)

μ: mean of weight

-Write a sentence using the confidence interval found in part a. (3 points)

We are 95% confident that true mean weight falls in the interval (3.2104, 3.3992).

-Use Minitab to construct a histogram of the sample data. Use the histogram to determine if the

assumption of normality is a valid assumption. State your findings. (4 points)

Histogram show the data are approximately normal.

-What sample size would be necessary to estimate the true weight with an error of ± 0.025 gram

with 90 percent confidence? (4 points)

Power and Sample Size

1-Sample t Test

Testing mean = null (versus ≠ null)

Calculating power for mean = null + difference

α = 0.1 Assumed standard deviation = 0.132

Results

Difference	Sample Size	Target Power	Actual Power
0.025	174	0.8	0.800581
0.025	241	0.9	0.900960

With 80% power we required a sample size of 174.