A cellphone provider has the business objective of wanting to determine the prop

Question

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 400400 subscribers. The results indicate that 9090 of the subscribers would upgrade to a new cellphone at a reduced cost. Reducing the price will be profitable if at least 20 %20% of the subscribers would upgrade. Complete parts (a) and (b) below. A.

At .05 level of significance, is there evidence that more then 20% of customers would upgrade?

What is the Zstat? The p-value is?

What is my final conclusion?

Explanation / Answer

Below are the null and alternate hypothesis

H0: p = 0.2

H1: p > 0.2

pcap = 90/400 = 0.225

SE = sqrt(0.2*0.8/400) = 0.02

Test statistics, z = (0.225 - 0.2)/0.02 = 1.25

p-value = 0.1056

As p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis.

There are not significanct evidence to conclude that at least 20% of the subscibers would upgrade.

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