Will Someone Please Help Me Solve This Statistics Question?

Question

Use two separate groups to create two population mean estimates (and let's assume the population is normally distributed). Ask a group of friends how much time (in hours) they spent on social media throughout the previous day. Divide this group into two subgroups (you must have at least 10 samples in each subgroup), and calculate the mean and standard deviation for both. Use the appropriate formula to construct a confidence interval to estimate the population mean. Then develop a response in which you address the following:

Group 1: (2,3,4,3,3,6,8,3,2,4)

Group 2: (3,3,2,2,6,6,2,2,1,1)

Present the confidence intervals you constructed from both subgroups (samples).

Compare and contrast these.

Relate the similarities and differences to the samples.

How do the groups differ?

How does the data differ between them?

How does this relate to the confidence intervals constructed from each?

Discuss which you feel is a more accurate estimate of the population mean and why.

Answer 1

Hello Taylor,

You can get the mean and standard deviation of both groups by using a graphing calculator (TI-80 series) or software. Computing standard deviation by hand is cumbersome. Remember, you want sample standard deviations (s), not population standard deviations (sigma). You also want the sample means xbar. From TI-83 Plus:

Group 1

xbar= 3.8

s= 1.87

Group 2

xbar= 2.8

s= 1.81

Now, let's compute the confidence intervals. For a normally distributed population, we can use a z-confidence interval, so formula is:

CI=xbar +/- z*SE

xbar=sample mean

z*=z-critical value

SE=standard error

Now, generally, 95% confidence is reasonable. Without knowing more, I cannot make any alternative recommendation, so let's go with that. z* for 95% confidence is 1.96, which you may want to memorize since 95% confidence intervals appear frequently in statistics.

Now, standard error (SE) has its own formula:

SE=s/sqrt(n)

s=sample standard deviation

n=sample size

Breaking this down for your samples:

Sample 1 Confidence Interval

xbar=3.8

z*=1.96

SE=s/sqrt(n)

s=1.87

n=10

SE=1.87/sqrt(10)

SE= 0.59

CI= 3.8 +/- (1.96*0.59)

CI = (2.64, 4.96)

Sample 2 Confidence Interval

xbar=2.8

z*=1.96

SE=s/sqrt(n)

s=1.81

n=10

SE=1.81/sqrt(10)= 0.57

CI= 2.8 +/- (1.96*0.57)

CI= (1.68, 3.92)

Now, I leave the interpretation questions to you. In the first case, we are 95% confident that true population mean falls between 2.64 and 4.96 hours. In the second, we are 95% confident that true population mean falls between 1.68 and 3.92 hours. Now that you understand what the intervals mean, interpret them as requested by your instructor. I hope this helps.