A pet food producer fills 25-pound bags of dog food on two different production lines located in separate cities. In an effort to determine whether differences exist between the average fill rates for the two lines, a random sample of 20 bags from line 1 and a random sample of 22 bags from line 2 were recently selected. Each bag's weight was measured and the accompanying table reports the summary measures from the samples. Assume the two lines are normally distributed with equal variances. Complete parts a through c below. LOADING... Click the icon to view the table of summary statistics from the samples. Production Production Line 1 Line 2 Sample Size, n 20 22 Sample Mean, x 25.28 25.49 Sample Standard Deviation, s 0.05 0.08 a. Calculate the point estimate for the difference between the population means of the two lines. Point estimate=nothing?? b. Develop a 90% confidence interval estimate of the true mean difference between the two lines. The 90% confidence interval is nothing??≤(μ1−μ2)≤nothing??. (Round to two decimal places as needed.) c. Based on the 90% confidence interval estimate calculated in part b, what can the managers of the production lines conclude about the differences bet

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.3: Measures Of Spread

Problem 8PPS

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A pet food producer fills 25-pound bags of dog food on two different production lines located in separate cities. In an effort to determine whether differences exist between the average fill rates for the two lines, a random sample of

bags from line 1 and a random sample of

bags from line 2 were recently selected. Each bag's weight was measured and the accompanying table reports the summary measures from the samples. Assume the two lines are normally distributed with equal variances. Complete parts a through c below.

Click the icon to view the table of summary statistics from the samples.

Production	Production
	Line 1	Line 2
Sample Size, n	20	22
Sample Mean, x	25.28	25.49
Sample Standard Deviation, s	0.05	0.08

a. Calculate the point estimate for the difference between the population means of the two lines.

Point

estimate=nothing??

b. Develop

90%

confidence interval estimate of the true mean difference between the two lines.

The

90%

confidence interval is

nothing??≤(μ1−μ2)≤nothing??.

(Round to two decimal places as needed.)

c. Based on the

90%

confidence interval estimate calculated in part b, what can the managers of the production lines conclude about the differences between the average fill rates for the two lines? Choose the correct answer below.

Since the interval

does not contain

zero, the two lines

may fill

bags with equal average amounts. The difference is at most about the magnitude of the

lower

limit.

Since the interval

does not contain

zero, the two lines

do not fill

bags with equal average amounts. The difference is at most about the magnitude of the

lower

limit.

Since the interval

does not contain

zero, the two lines

do not fill

bags with equal average amounts. The difference is at most about the magnitude of the

upper

limit.

Since the interval

does not contain

zero, the two lines

may fill

bags with equal average amounts. The difference is at most about the magnitude of the

upper

limit.

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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