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izaiahfieods
18.02.2020 •
Mathematics
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.
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Ответ:
1. Null hypotheses: p=0.49
Alternative hypotheses: p>0.49
2. p=0.5704 or 57.04%
Step-by-step 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%
Ответ: