To: Chen Cheng, Ph.D., [Instructor]
From: Ali Dasouqi, [Engineering Manager]
Date: September 25th 2022
Subject: PFC Princess Select Product Release Investigation
cc: Di An & Lingyi Zheng, [Teaching Assistants]
Hypothesis testing on a sample of 200 customers, of whom nearly 62% are interested in
subscribing to the new service for an average price of $49.2, encourage the marketing and
release of the new product. Considering at least 75% satisfied customers who are willing to
pay at least $49 is a feasible claim as the analysis supports the hypothesized parameters to
succeed. The critical values for the price ($48.46) and proportion (69.95%) falling below the
targeted values indicates the new service success.
Forming the Hypothesis
The larger sample size of 200 customers helps to obtain a smaller sampling error. The sample
mean and standard deviation were given as $49.2 and 4.6, respectively. In order to support the
release and marketing of the new service, hypothesis testing was demonstrated in the appendix
assuming a selling price of at least $49 and 75% interested customers with a significance level
of 10%. Specifically, calculating the critical values for the price ($48.46) and proportion (69.95%)
using the z-based distribution tables allow comparisons to be made among the targeted
parameters. The null hypothesis was supported due to the previously mentioned reasoning and
as shown below.
Appendix
Statistics
µo
sample mean
n
sample error
standard deviation
Po
r
σP
α
z
Price
Proportion
49
49.2
200
0.325269119
4.6
0.75
0.62
0.030618622
0.1
-1.65
Ho
µo ≥ 49
support Xc = µo - z*(σ/sqrt(n))
Ha
µo < 49
Reject
Ho
Po ≥ 75%
support Pc = Po - (z* σP)
Ha
Po < 75%
Reject
48.463
0.6995