The mean crying time of infants during naptime at a local preschool is 12 minutes.The school implements a new naptime routine in a sample of 25 infants and records an average crying time of 8±4.6 (M±SD)minutes.Test whether this new naptime routine reduced crying time at a .05 level of significance. A)The new naptime routine significantly reduced crying time,t(24)= -4.35,p

Question

The mean crying time of infants during naptime at a local preschool is 12 minutes.The school implements a new naptime routine in a sample of 25 infants and records an average crying time of 8±4.6 (M±SD)minutes.Test whether this new naptime routine reduced crying time at a .05 level of significance.
A)The new naptime routine significantly reduced crying time,t(24)= -4.35,p < .05.
B)The new naptime routine did not reduce crying time,t(24)= -4.35,p < .05.
C)The new naptime routine did not reduce crying time,t(24)= 0.92,p > .05.
D)The new naptime routine significantly reduce crying time,t(24)= 0.92,p < .05.

Quizplus · Accepted Answer

To test whether the new naptime routine reduced crying time, we need to conduct a one-sample t-test comparing the sample mean (8) to the population mean (12). We are given that the sample size is 25, so we have 24 degrees of freedom (df = n-1). 
The formula for calculating the t-value is: 
t = (sample mean - population mean)/(standard error) 
The standard error is calculated as: 
SE = SD/sqrt(n) 
where SD is the sample standard deviation, and n is the sample size. 
Plugging in the values, 
t = (8-12)/(4.6/sqrt(25)) 
t = -4.35 
At a significance level of .05, with 24 degrees of freedom, the critical t-value is ±1.711. Since our calculated t-value (-4.35) falls outside this range, we can reject the null hypothesis and conclude that the new naptime routine significantly reduced crying time. Therefore, the best choice is A.

The Mean Crying Time of Infants During Naptime at a Local