Answered: Workers at a certain soda drink factory…

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.3: Measures Of Spread

Problem 26PFA

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Question

Workers at a certain soda drink factory collected data on the volumes (in ounces) of a simple random sample of 21 cans of the soda drink. Those volumes have a mean of 12.19 oz and a standard deviation of 0.14 oz, and they appear to be from a normally distributed population. If the workers want the filling process to work so that almost all cans have volumes between 11.88 oz and 12.52

oz, the range rule of thumb can be used to estimate that the standard deviation should be less than 0.16

Use the sample data to test the claim that the population of volumes has a standard deviation less than 0.16 oz. Use a 0.05 significance level. Complete parts (a) through (d) below.

38. Workers at a certain soda drink factory collected data on the volumes (in ounces) of a simple random sample of 21 cans of the soda drink. Those volumes have a
mean of 12.19 oz and a standard deviation of 0.14 oz, and they appear to be from a normally distributed population. If the workers want the filling process to work so
that almost all cans have volumes between 11.88 oz and 12.52 oz, the range rule of thumb can be used to estimate that the standard deviation should be less than
0.16 oz. Use the sample data to test the claim that the population of volumes has a standard deviation less than 0.16 oz. Use a 0.05 significance level. Complete
parts (a) through (d) below.
a. Identify the null and alternative hypotheses. Choose the correct answer below.
O A. Ho: >0.16 oz
H₁: a = 0.16 oz
O C. Ho: o=0.16 oz
H₁: <0.16 oz
b. Compute the test statistic.
x² =
(Round to three decimal places as needed.)
c. Find the P-value.
P-value=
(Round to four decimal places as needed.)
d. State the conclusion.
(1)
Ho, because the P-value is (2).
standard deviation of can volumes is less than 0.16 oz.
(1) O Reject
O Do not reject
(2) ○ less than or equal to
O greater than
(3)
O B. Ho: gà 0.16 oz
H₁: o <0.16 oz
sufficient
insufficient
O D. Ho: 0.16 oz
H₁: o *0.16 oz
the level of significance. There is (3)
evidence to conclude that the population

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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