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Eva8 [605]
2 years ago
14

A major videocassette rental chain is considering opening a new store in an area that currently does not have any such stores. T

he chain will open if there is evidence that more than 5,000 of the 20,000 households in the area are equipped with videocassette recorders (VCRs). It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have VCRs. At =2.5% and sample data, what would be your recommendation to the rental chain management?
a. Since the critical test value is 1.96, we are going to reject the null hypothesis. The rental chain store should open a store in this area.
b. Since the critical test value is 1.96, we have failed to reject the null hypothesis. The rental chain store should not open a store in this area.
c. Since the critical test value is 1.96, we have failed to reject the null hypothesis. The rental chain store should not open a store in this area.
d. Since the critical test value is 1.96, we have failed to reject the null hypothesis. The rental chain store should open a store in this area.
Mathematics
1 answer:
iren [92.7K]2 years ago
4 0

Answer:

Step-by-step explanation:

Population proportion, p = 5000/20000 = 0.25

We would set up the hypothesis test.

For the null hypothesis,

p = 0.25

For the alternative hypothesis,

p > 0.25

Considering the population proportion, probability of success, p = 0.25

q = probability of failure = 1 - p

q = 1 - 0.25 = 0.75

Considering the sample,

Sample proportion, P = x/n

Where

x = number of success = 96

n = number of samples = 300

P = 96/300 = 0.32

We would determine the test statistic which is the z score

z = (P - p)/√pq/n

z = (0.32 - 0.25)/√(0.25 × 0.75)/300 = 2.8

The calculated test statistic is 2.8 for the right tail and - 2.8 for the left tail

Since α = 0.025, the critical value is determined from the normal distribution table. The z score for the lower and upper tail of the curve is - 1.96 and 1.96

In order to reject the null hypothesis, the test statistic must be smaller than - 1.96 or greater than 1.96

Since - 2.8 < - 1.96 and 2.8 > 1.96, we would reject the null hypothesis.

Therefore, the correct option is

a. Since the critical test value is 1.96, we are going to reject the null hypothesis. The rental chain store should open a store in this area.

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Which of following lies between 0 and -1 ?
kogti [31]

Answer:

Step-by-step explanation:

There are many numbers that lie between 0 and -1

Some common numbers are -1/4 , -1/2 , -3/4 , etc.........

Other numbers can be found by multiplying the numerator and denominator by the same number for example, 10

0/1 × 10/10 = 0/10

-1/1 × 10/10 = -10/10

Now the numbers between 0/10 and -10/10 are :

-1/10, -2/10....................................-9/10 etc.

hope this helps

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6 0
2 years ago
Ann's car can travel 228 miles on 6 gallons of gas. a. Write an equation to represent the distance, y, in miles Ann's car can tr
Murrr4er [49]

Answer:

288 gallons ÷ 6 miles = 48 miles per gallon  

48 miles per gallon • 7 miles = 366 miles  

Step-by-step explanation:

7 0
2 years ago
Simplify 12 1/3b + 6 2/3 - 10 2/3b
slavikrds [6]

Answer:

1 2/3b + 6 2/3

Step-by-step explanation:

12\frac{1}{3}b+6\frac{2}{3}-10\frac{2}{3}b

Combine like terms:

1\frac{2}{3}b+6\frac{2}{3}

Since you cannot do any more combination or simplification, you are done. Hope this helps!

4 0
2 years ago
The Smiths bought new furniture that cost $3,298.00. The store offered them
ad-work [718]

Answer:

10.99%.

Step-by-step explanation:

We have been given that the Smiths bought new furniture that cost $3,298.00. The store offered them  an option of putting $600 down and making equal payments of $300 a month  for 10 months.

First of all, we will find amount paid by down-payments in 10 months.

\$300\times 10=\$3,000

Total amount paid by Smiths: \$3,000+\$600=\$3,600.

Now we will find amount paid in interest by subtracting initial amount from total amount.

\text{Amount paid in interest}=\$3,600-\$3,298

\text{Amount paid in interest}=\$302

10 months = 10/12 year =5/6 year.

Now, we will use simple interest formula to solve for interest rate.

I=Prt

\$302=\$3,298*r*\frac{5}{6}

\$302=r*\frac{\$16,490}{6}

\$302*\frac{6}{\$16,490}=r*\frac{\$16,490}{6}*\frac{6}{\$16,490}

\frac{1,812}{\$16,490}=r

r=\frac{1,812}{\$16,490}

r=0.1098847786

r=0.1098847786\times 100

r=10.98847786\%

r\approx 10.99\%

Therefore, the annual interest rate is 10.99%.

7 0
2 years ago
Milton spilled some ink on his homework paper. He can't read the coefficient of $x$, but he knows that the equation has two dist
Lera25 [3.4K]

Answer:

Sum = -81

Step-by-step explanation:

See the comment for complete question.

Given

c = 36 ----- Constant

No coefficient of x^2

Required:

Determine the sum of all distinct positive integers of the coefficient of x

Reading through the complete question, we can see that the question has 3 terms which are:

x^2 ---- with no coefficient

x ---- with an unknown coefficient

36 ---- constant

So, the equation can be represented as:

x^2 + ax + 36 = 0

Where a is the unknown coefficient

From the question, we understand that the equation has two negative integer solution. This can be represented as:

x = -\alpha and x = -\beta

Using the above roots, the equation can be represented as:

(x + \alpha)(x + \beta) = 0

Open brackets

x^2 + (\alpha + \beta)x + \alpha \beta = 0

To compare the above equation to x^2 + ax + 36 = 0, we have:

a = \alpha + \beta

\alpha \beta = 36

Where: \alpha, \beta and \alpha \ne \beta

The values of \alpha and \beta that satisfy \alpha \beta = 36 are:

\alpha = -1 and \beta = -36

\alpha = -2 and \beta = -18

\alpha = -3 and \beta = -12

\alpha = -4 and \beta = -9

So, the possible values of a are:

a = \alpha + \beta

When \alpha = -1 and \beta = -36

a = -1 - 36 = -37

When \alpha = -2 and \beta = -18

a = -2 - 18 = -20

When \alpha = -3 and \beta = -12

a = -3 - 12 = -15

When \alpha = -4 and \beta = -9

a = -4 - 9 = -13

At this point, we have established that the possible values of a are: -37, -20, -15 and -9.

The required sum is:

Sum = -37 -20 -15 - 9

Sum = -81

7 0
2 years ago
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