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In a random sample of 48 people, the mean body mass index (BMI) was 28.3 and the standard deviation was 6.01.

In a random sample of 48 people, the mean body mass index (BMI) was 28.3 and the standard deviation was 6.01.

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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Y6.2.35-T Assigned Media Question Help Use the standard normal distribution or the t-distribution to construct a 95% confidence interval for the population mean. Justify your decision. If neither distribution can be used, explain why. Interpret the results. In a random sample of 48 people, the mean body mass index (BMI) was 28.3 and the standard deviation was 6.01. Which distribution should be used to construct the confidence interval? Choose the correct answer below. A. Use a t-distribution because the sample is random, the population is normal, and o is unknown. B. Use a normal distribution because the sample is random, the population is normal, and o is known. C. Use a t-distribution because the sample is random, n2 30, and o is unknown. D. Use a normal distribution because the sample is random, n2 30, and o is known. er a normal distribution nor a t-distribution can be used because either the sample is not random, or n< 30, and the population is not known to be normal. rf Select the correct choice below and, if necessary, fill in any answer boxes to complete your choice. O A. The 95% confidence interval is ( ). (Round to two decimal places as needed.) B. Neither distribution can be used to construct the confidence interval. gree Click to select and enter your answer(s) and then click Check Answer. へ@ e Type here to search PrtScn 17 Home FB End PgUp FS F6 4. 5 8. to
Transcribed Image Text:Y6.2.35-T Assigned Media Question Help Use the standard normal distribution or the t-distribution to construct a 95% confidence interval for the population mean. Justify your decision. If neither distribution can be used, explain why. Interpret the results. In a random sample of 48 people, the mean body mass index (BMI) was 28.3 and the standard deviation was 6.01. Which distribution should be used to construct the confidence interval? Choose the correct answer below. A. Use a t-distribution because the sample is random, the population is normal, and o is unknown. B. Use a normal distribution because the sample is random, the population is normal, and o is known. C. Use a t-distribution because the sample is random, n2 30, and o is unknown. D. Use a normal distribution because the sample is random, n2 30, and o is known. er a normal distribution nor a t-distribution can be used because either the sample is not random, or n< 30, and the population is not known to be normal. rf Select the correct choice below and, if necessary, fill in any answer boxes to complete your choice. O A. The 95% confidence interval is ( ). (Round to two decimal places as needed.) B. Neither distribution can be used to construct the confidence interval. gree Click to select and enter your answer(s) and then click Check Answer. へ@ e Type here to search PrtScn 17 Home FB End PgUp FS F6 4. 5 8. to
Expert Solution
Step 1 - Writing given data

Given that

Random sample size(n) =48

Mean body mass index (x¯)=28.3

Sample standard deviation (s) =6.01

Confidence level (C)= 95% = 0.95

Level of significance (α) = (1-0.95) = 0.05

We use t-distribution because the sample is random and population standard deviation is unknown.

Critical value (t(α2))

Degrees of freedom (df) =n-1

                         df = 48-1 =47

From t-table

At α2 = 0.025 ; df=47 ; One-tailed test

t(α2) = 2.01 =tc (t-critical value)

 

 

 

 

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