Chapter 9 Question 7 A cellphone provider has the business objective of wanting
ID: 3178724 • Letter: C
Question
Chapter 9 Question 7
A cellphone provider has the business objective of wanting to determine the proportion of subscribers who would upgrade to a new cellphone with improved features if it were made available at a substantially reduced cost. Data are collected from a random sample of
600 subscribers. The results indicate that 137 of the subscribers would upgrade to a new cellphone at a reduced cost. Reducing the price will be profitable if at least 20%
of the subscribers would upgrade. Complete parts (a) and (b) below.
a. At the 0.01 level of significance, is there evidence that more than 20%
of the customers would upgrade to a new cellphone at a reduced cost?
To answer this question, start by setting up the null and alternative hypotheses for the population proportion .
Now identify the level of significance =
Find the z stat-
Identify sample size n, the number of events of interest X, and calculate n-x
Is the hypothesis a one-tail or two tail test?
What is the p-value
b. How would the manager in charge of promotional programs concerning cellphone upgrades use the results in (a)? Consider the conclusion from the hypothesis test in part (a). Remember that reducing the price will be profitable if more than 20%
of the subscribers would upgrade.
Explanation / Answer
H0 : .20
H1 : > .20 (Claim)
= 0.05
One-tailed test(because H1 ">". If H1 "=", then would be two-tailed test)
X=137
n =600
= 137/600=0.23
q = 463/600=0.77
Using Graphing Calculator TI-83: Go to STATS, TESTS, 5:1-PropZTest, 0: .20, X: 137, n: 600, prop >0, Calculate.
Since p-value = 0.0000 which is less than the level of significance =0.05. Therefore, reject H0 and support the claim that more than 20% of customers would upgrade to a new cell phone at a reduced cost.
The manager would go ahead and promote new cellphones at a reduced rate based on these results.