Question

The folks at Purple Passion Perfume (P3) want to estimate the unknown average age u, of all P3 customers. A random sample of n = \27 P3 customers had mean age i = 28.7 with st dev s = 1.48. i) Find a95% Confidence Interval (CD for p ii) Interpret your interval. iii) Is p in this CI? Why or why not? Explain.

Answer 1

i) Given A random sample of n = 27 P3 customers had mean age M = 28.7 with standard deviation = 1.48, since the sample size is less than 30 and population standard deviation is not known hence t-distribution is applicable for confidence interval calculation.

The confidence interval is calculated as:

μ = M ± t(s_M)

where:

M = sample mean
t = t statistic determined by confidence level
s_M = standard error = √(s²/n)

n = Sample size

df = n-1

Now the calculations:

M = 28.7
t = 2.06 calculated using the excel formula for t-distribution which takes the degree of freedom and the signficance level as the parameters. The formula used is =T.INV.2T(0.05, 26)
s_M = √(1.48²/27) = 0.28

μ = M ± t(s_M)
μ = 28.7 ± 2.06*0.28
μ = 28.7 ± 0.585

Thus the confidence interval is computed as:

{ 28.115, 29.285 }

ii) Interpretation:

We are 95% confident that the true population mean will lie within the calculated confidence interval which is { 28.115, 29.285 }.

iii) Is p in this CI?

No, becuase the p is the proportion of the sample and here the details are given of the mean and population mean confidence interval can be calculated using the given details.

Note: Feel free to ask if query remains

answered by: anonymous