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%

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

the data of the detroit pistons in numerical order from least to greatest is 0.30, 0.37, 0.55, 0.62, 0.69, 0.72, 0.73, 0.75, 0.77, 0.78, 0.80, 0.81, 0.81, 0.83, 0.84, 0.89

the data of the miami heat in numerical order from least to greatest is 0.50, 0.50, 0.56, 0.57, 0.67, 0.72, 0.72, 0.72, 0.75, 0.75, 0.76, 0.81, 0.82, 0.90, 1.00, 1.00

the detroit pistons median : 1.52

the miami heat median: 1.47

the iqr of this data is 0.05