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A nutrition lab tested 40 hot dogs to see if their mean sodium content was less than the 325-mg upper limit set by regulations for "reduced sodium" franks. The mean sodium content for the sample was 321.8 mg with a standard deviation of 17 mg. Assume that the assumptions and conditions for the test are met. (a) Test the hypothesis that the mean sodium content meets the regulation. (i) Ho ; HA: (ii) Perform the test and find the P-value. The test statistic is t = The P-value is

A nutrition lab tested 40 hot dogs to see if their mean sodium content was less than the 325-mg upper limit set by regulations for "reduced sodium" franks. The mean sodium content for the sample was 321.8 mg with a standard deviation of 17 mg. Assume that the assumptions and conditions for the test are met. (a) Test the hypothesis that the mean sodium content meets the regulation. (i) Ho ; HA: (ii) Perform the test and find the P-value. The test statistic is t = The P-value is

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.5: Comparing Sets Of Data
Problem 13PPS
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(8) A nutrition lab tested 40 hot dogs to see if their mean sodium content was less than the 325-mg upper limit set by regulations for "reduced sodium" franks. The mean sodium content for the sample was 321.8 mg with a standard deviation of 17 mg. Assume that the assumptions and conditions for the test are met. (a) Test the hypothesis that the mean sodium content meets the regulation. (i) Ho: ; HA: (ii) Perform the test and find the P-value. The test statistic is t = The P-value is (iii) State your conclusion. Use a = 0.05. the null hypothesis. There (is, is not) sufficient evidence to conclude that the mean sodium content is from, different from) the value specified in the regulation. (less than, greater than, not different (b) Will a larger sample size ensure that the regulations are met? A. No. Although the sample mean is less than the limit, increasing the sample size will increase the standard error, so the test will not become more specific. B. No. If another larger sample is chosen, the sample mean could be larger or smaller than the limit. C. Yes, because the sample mean is less than the limit. Increasing the sample size will decrease the sample standard deviation, which will decrease the p-value. D. Yes, because the sample mean is less than the limit. Increasing the sample size will decrease the standard error, which will decrease the p-value.
Transcribed Image Text:(8) A nutrition lab tested 40 hot dogs to see if their mean sodium content was less than the 325-mg upper limit set by regulations for "reduced sodium" franks. The mean sodium content for the sample was 321.8 mg with a standard deviation of 17 mg. Assume that the assumptions and conditions for the test are met. (a) Test the hypothesis that the mean sodium content meets the regulation. (i) Ho: ; HA: (ii) Perform the test and find the P-value. The test statistic is t = The P-value is (iii) State your conclusion. Use a = 0.05. the null hypothesis. There (is, is not) sufficient evidence to conclude that the mean sodium content is from, different from) the value specified in the regulation. (less than, greater than, not different (b) Will a larger sample size ensure that the regulations are met? A. No. Although the sample mean is less than the limit, increasing the sample size will increase the standard error, so the test will not become more specific. B. No. If another larger sample is chosen, the sample mean could be larger or smaller than the limit. C. Yes, because the sample mean is less than the limit. Increasing the sample size will decrease the sample standard deviation, which will decrease the p-value. D. Yes, because the sample mean is less than the limit. Increasing the sample size will decrease the standard error, which will decrease the p-value.
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