The mean of the data is 14.8 while the standard deviation is 6.7646138. It means that on average, people spend 14.8 hours per week on cleaning. The standard deviation of 6.7646 shows the spread of the data from the actual mean.
Using t-statistic, the confidence interval can be given as
S= 6.7646138, n= 25, apha= 5%, t0.025, 24= 2.064
µ = 14.8 ± [2.064*(6.7646138/5)
µ = 14.8 ± 2.7924
µ = [12.0076, 17.5924]
We are 95% confident that the true the population mean number of hours per week lies between 12.0076 hrs and 17.5924 hrs.
Bonus Questions
Question One
a)
Since the researcher used simple random sampling technique to obtain a sample of 100 emails out of the total 1000 emails using the random number table, the sample is a representation of all the registered voters. However, using the formula for deriving the sample size of a finite population at 5% level of significance, ;
== 375
The correct sample size should have been 375 emails and not 100 emails.
b)
The problem with classes is that they are overlapping thereby making it difficult to determine the class limits. The classes should be organized as follows;
Class Frequency
0-2
3-5
6-8
9-11
12-14
Question Two
a)
The probability that a student is female and lives in dorm is given by;
P(female and lives in dorm)= P(female)*p(female in dorm)= (500/1000) * (210/500) = 0.21
b)
The probability that a student is female given that she lives in a dorm is given by;
P(F/Dorm)= P (Female and Dorm)/P (female living in Dorm)= (.5*.36)/.21 = 0.8571
