Answered: Data on the weights (lb) of the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Data on the weights (lb) of the contents of cans of diet soda versus the contents of cans of the regular version of the soda is summarized to the right. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.05 significance level for both parts.			Diet	Regular
μ	μ1	μ2
n	20	20
x	0.78646 lb	0.80233 lb
s	0.00449 lb	0.00755 lb

a. Test the claim that the contents of cans of diet soda have weights with a mean that is less than the mean for the regular soda.

What are the null and alternative hypotheses?

H0:

μ1=μ2

H1:

μ1≠μ2

H0:

μ1=μ2

H1:

μ1>μ2

H0:

μ1≠μ2

H1:

μ1<μ2

H0:

μ1=μ2

H1:

μ1<μ2

The test statistic, t, is

nothing.

(Round to two decimal places as needed.)

The P-value is

nothing.

(Round to three decimal places as needed.)

State the conclusion for the test.

Reject

the null hypothesis. There

sufficient evidence to support the claim that the cans of diet soda have mean weights that are lower than the mean weight for the regular soda.

Reject

the null hypothesis. There

is not

sufficient evidence to support the claim that the cans of diet soda have mean weights that are lower than the mean weight for the regular soda.

Fail to reject

the null hypothesis. There

is not

sufficient evidence to support the claim that the cans of diet soda have mean weights that are lower than the mean weight for the regular soda.

Fail to reject

the null hypothesis. There

sufficient evidence to support the claim that the cans of diet soda have mean weights that are lower than the mean weight for the regular soda.

b. Construct a confidence interval appropriate for the hypothesis test in part (a).

nothing

lb<μ1−μ2<

nothing

(Round to three decimal places as needed.)

Does the confidence interval support the conclusion found with the hypothesis test?

▼

No,

Yes,

because the confidence interval contains

▼

only negative values.

only positive values.

zero.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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