Respuesta :
Answer:
a) There is evidence that more than 20% of the customers would upgrade to a new cellphone at a reduced cost
b) The manager in charge of promotional programs concerning residential customers will help the customers to upgrade their cellphones at a reduced cost.
Step-by-step explanation:
sample size, n = 500
The number of subscribers who would upgrade to a new cellphone at reduced cost, X = 135
Proportion of those that would upgrade to a new cellphone,
[tex]\hat{p} = \frac{X}{n} \\\hat{p} = 135/500\\\hat{p} = 0.27[/tex]
The null hypothesis is that less than or equal to 20%( i.e. 0.2) of the customers would upgrade to a new cellphone at a reduced cost while the alternative hypothesis is that more than 20% would upgrade to a new cellphone at a reduced cost.
Null hypothesis, [tex]H_{0} : p \leq 0.20[/tex]
Alternative hypothesis, [tex]H_{a} : p > 0.20[/tex]
The test statistic can be calculated as thus:
[tex]z_{test} = \frac{\hat{p} - p_{0} }{\sqrt{\frac{p_{0}(1 - p_{0}) }{n} } }[/tex]
[tex]z_{test} = \frac{0.27 - 0.20}{\sqrt{\frac{0.20(1 -0.20)}{500} } }[/tex]
[tex]z_{test} = 3.913[/tex]
To get the p - value for the test statistic:
[tex]p(z > 3.913) = 1 - p(z \leq 3.913)\\p(z \leq 3.913) = 0.999954 ( from the distribution table)\\p(z > 3.913) = 1 - 0.999954\\p(z > 3.913) =0.000046[/tex]
Since the p - value is less than 0.05 significance level, the null hypothesis will be rejected. (i.e. more than 20% would upgrade to a new cellphone at a reduced cost.)
