Question

Records for the past several years show that 46% of customers at a local game shop use a customer loyalty card. Due to a recent promotion of the cards, the manager wants to know if the percentage has increased. The manager decides to take a simple random sample of 135 customers and finds that 77 of them used the customer loyalty card at their last transaction. Round all numeric results to 4 decimal places.

1, Write the hypotheses to test if the proportion of customers using the card has increased from 49%.
2. Calculate the proportion of customers in the sample who used the loyalty card.

Answer 1

1. Null hypotheses: p=0.49

Alternative hypotheses: p>0.49

2. p=0.5704 or 57.04%

Explanation:

1.

We have to writer the hypotheses for testing the proportion has increased from 49%. So, the population proportion that is to be tested is 0.49.

As we already know that the null hypotheses always contain equality so,

Null hypotheses: p=0.49

and we have to test whether the proportion has increased from 0.49, so,

Alternative hypotheses: p>0.49

Thus, the hypotheses for testing the proportion has increased from 49% are

Null hypotheses: p=0.49

Alternative hypotheses: p>0.49

2.

We have to find the proportion of sampled customers using loyalty card.

The given sample indicate that 77 out of 135 customers are using loyalty card. So,

p=x/n

where x is the number of favorable outcome and n is total number of outcome.

Here, x=77 and n=135. So,

p=77/135=0.5704 or 57.04%