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.

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%

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

the radius is 2 times the diameter.

step-by-step explanation: