Question

Topical Painkiller Ointment

The use of topical painkiller ointment or gel rather than pills for pain relief was approved just within the last few years in the US for prescription use only.¹ Insurance records show that the average copayment for a month's supply of topical painkiller ointment for regular users is $30. A sample of size n=75 regular users found a sample mean copayment of $27.90.

(a) Identify each of 30 and 27.90 as a parameter or a statistic.

(b) Give the appropriate notation for 30

(c) Give the appropriate notation for 27.90

(d) If we take 1000 samples of size n=75 from the population of all copayments for a month's supply of topical painkiller ointment for regular users and plot the sample means on a dotplot, describe the shape you would expect to see in the plot and where it would be centered.

The shape of the plot will be ____and the center will be at ____.

(e) How many dots will be on the dotplot you described in part (d)?
_____ dots

Answer 1

Given the average payment for a month's supply of topical painkiller ointment for regular users is $30.

A sample of n= 75 regular users found a sample mean copayment of $ 27.90

a. Hare the 30 is a population parameter.

Parameter is a quantity which describes the population of interest.

And 27.90 is a statistic. Statistic is a numerical quantity which describes the sample based on which inference about the the population are drawn.

b. The appropriate notation for 30 is

c. The appropriate notation for 27.90 is

d. If we take 1000 sample of size n= 75 from the population of all copayments for month's supply of topical painkiller ointment for regular users and plot sample means on the dot plot.

The shape of the dot blot is approximately symmetry and the centre will be at the value of 30.

Since, according to the central limit theorem as n is sufficient large the sampling distribution of sample mean is approximately normally with mean equal to .

e. There will be 1000 dots on the dot plot. Since we plot the sample means of 1000 sample of size n=75 on the dot plot, there will be 1000 dots.