roblem The following data are taken from a study investigating the length of tim
ID: 3356104 • Letter: R
Question
roblem The following data are taken from a study investigating the length of time in days between the occurrence of the injury and the first magnetic resonance imaging (MRI).The data are shown in the following table: Subject Days Subject Days Subject Days Subject Days 14 28 24 24 16 17 12 13 14 15 10 18 26 12 10 21 Compute a point estimate for mean number of days between injury and initial MRI and standard error of the mean. a. Test whether the mean number of days between injury and initial MRI is not 14 days in a population presumed to be represented by these sample data? b. c. Interpret your answer in a Find the 95% confidence interval of the mean number of days between injury and initial MRI? d e. Explain what does "a 95% confidence" meansExplanation / Answer
(a) Point estimate of Mean number of days between injury = sample mean = 13.294 days
Sample standard deviation s = 8.8865 days
standard error of the sample mean se0 = s/ sqrt(n) = 8.8865/sqrt(17) = 2.1553 days
(b) H0 : = 14 days
Ha : 14 days
Test statistic
t = (x - H)/ se0 = (13.294 - 14)/ 2.1553 = -0.33
Here dF = 16, alpha a = 0.05
tcritical = 2.12
l t l < tcritical so we shalln't reject the null hypothesis and say population mean is still 14 days.
(iii) Here we can say that mean days of stay between injury and initial MRI is 14 days.
(iv) 95% confidence interval= x +- tcritical se0
= 13.294 +- 2.12 * 2.1553
= (8.725, 17.863)
(e) Here 95% confidence mean that if we take sample size of 17 repeateadly then it is 95% probability that average days between injuryand initial MRI shall be in between 95% confidence interval.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.