MATHEMATICS HIGH SCHOOL

A manager of a grocery store wants to determine if consumers are spending more than the national average. The national average is $150.00 with a standard deviation of $30.20. The manager collects 40 random receipts and finds that the average is $160. Complete a hypothesis test with a significance level of 2.5% to determine if the average customer spends more in his store than the national average. Which of the following is a valid conclusion for the manager based on this test?a.The customers spend more than the national average in his store.b.The manager should decrease prices in his store.c.The customers do not spend more than the national average in his store.d.The customers in his store just come from a rich neighborhood.

Answers

Answer 1

Answer:

Answer:

The correct answer is:

The customers spend more than the national average in his store

Step-by-step explanation:

The national average is $150.00 with a standard deviation of $30.20.

Sample size n =40

H0: x bar = mu

Ha: x bar >mu

(one tailed test for a single mean)

Sample average x bar = 160

Mean difference = 160-150 =10

std error = 30.20/sqrt 40

=4.775

Test statistic = 2.094

Z critical for 2.5% = 1.96 (one tailed)

Since test statistic > z critical we reject null hypothesis.

Hence the correct answer is:

The customers spend more than the national average in his store.

Answer 2

Answer:

Answer:

Option A) The customers spend more than the national average in his store.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = $150.00

Sample mean, $\bar{x}$ = $160

Sample size, n = 40

Alpha, α = 0.025

Population standard deviation, σ = $30.20

First, we design the null and the alternate hypothesis

$H_(0): \mu = 150\text{ dollars}\nH_A: \mu > 150\text{ dollars}$

The null hypothesis states that the consumers are spending equal to the national average. The alternative hypothesis states that consumers are spending more than the national average.

We use One-tailed z test to perform this hypothesis.

Formula:

$z_(stat) = \displaystyle\frac{\bar{x} - \mu}{(\sigma)/(√(n)) }$

Putting all the values, we have

$z_(stat) = \displaystyle(160 - 150)/((30.20)/(√(40)) ) = 2.094$

Now, $z_(critical) \text{ at 0.025 level of significance } = 1.96$

Since,

$z_(stat) > z_(critical)$

We reject the null hypothesis and accept the alternate hypothesis. Thus, the customers spend more than the national average in his store.

Thus, option A) is a valid conclusion for the manager

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The curve produced by the water coming from a hose is sketched onto a graph with zeros at 0 and 5. The point (4, 1) also lies on the curve. If h(x) represents the vertical distance from where the water first comes out of the hose and x represents the horizontal distance, which statements are true? Check all that apply.A.The scenario can be represented by the function h(x) = –0.25(x)(x – 5). B.The scenario can be represented by the function h(x) = (x)(x + 5). C.The vertex is on the line x = 2.5. D.The greatest height that the water reaches is 1.5 units. E.The scenario can be represented by the function h(x) = –1(x – 5).

Stacy goes to the county fair with her friends. The total cost of ride tickets is given by the equation c = 3.5t, where c is the total cost of tickets and t is the number of tickets. If Stacy bought 15 tickets, she would spend

Answers

Answer:

Stacy would spend $52.50 in buying the tickets.

Step-by-step explanation:

The total cost of tickets brought can be calculated by the formula c=3.5 t.

Here t represents the number of tickets .

It is given Stacy bought 15 tickets ,hence t=15.

The total cost of tickets Stacy bought c= 3.5(15)

Or c=52.5

Stacy would spend $52.50 in buying the tickets.

c = 3.5(15)
c = 52.50

A figure is triangular in shape and is semicircular at the bottom. find perimeter and area of figure

Answers

fr we need the measurements to do the work bro

a couch sells for $1260. instead of paying the toatl amount at the time of the purchase, the same couch can be brought by paying 400 down and 80 a month for 12 months. how much is saved by paying the total amount at the time of the purchase

Answers

Answer:

$100 can be saved.

Step-by-step explanation:

A couch sells for = $1260

The same couch can be brought by paying 400 down payment and $80 per month for 12 months.

Total amount will be paid = 400 + (80× 12)

= 400 + 960

= $1,360

Difference between the amounts = 1360 - 1260

= $100

You can save $100 by paying the total amount at the time of the purchase.

If you pay $400 down, plus $80 for the next 12 months, that means you're paying (80*12)+400 which is equal to $1360. You're saving $100 by paying the entire total up front.

your employer has 600 business cards printed for you and you give away 280 of them to the nearest hundred what percent of the cards is left

Answers

First, find the number of cards that is left. 600 - 280 = 320.

Now find what percent of 600 320 is. This can be done like so:
$(280)/(600)$ · 100%

This gives us 46.67 % (rounded to the nearest hundredth).

Every 4 seconds, a ski lift chair rises 14 feet. Describe the relationship between the height of the chair and the time.

Answers

The relationship between the rise of the chair with respect to time is required.

The ski lift chair rises $3.5\ \text{feet/s}$

Rate of change

Every $4$ seconds a ski lift chair rises $14\ \text{feet}$ .

$4\ \text{seconds}=14\ \text{feet}$

Divide by $4$ on both sides

$1\ \text{second}=(14)/(4)=3.5\ \text{feet}$

The rate of the height increase of the ski lift chair is $3.5\ \text{feet/s}$

Learn more about rate of change:

brainly.com/question/8728504

Emma earns $6 each time she mows the lawn and $8 per hour for babysitting. She is saving up to buy a new pair of jeans that cost $48. If she mows the lawn x times and babysits for y hours, which graph shows the amount of work she needs to complete to earn at least enough to purchase the new jeans?

Answers

To graph this we find the x- and y-intercepts. The x-intercept would be at 8 and the y-intercept would be at 6.

Explanation:
The equation is 6x+8y=48. An x-intercept is the point where the data crosses the x-axis. All points on this line will have a y-coordinate of 0, so we replace y with 0 and solve:
6x+8(0)=48
6x=48.

Divide both sides by 6:
6x/6=48/6
x=8.
We go to 8 on the x-axis and plot the point.

A y-intercept is the point where the data crosses the y-axis. All points on this line will have an x-coordinate of 9, so we replace x with 0 and solve: 6(0)+8y=48
0+8y=48
8y=48.

Divide both sides by 8:
8y/8 = 48/8
y=6.

We go up to 6 on the y-axis and plot the point. We then draw a line through these two points.

Answer:

Refer the figure.

Step-by-step explanation:

Let x be the number of times Emma mows the lawn

and y be the number of hours Emma babysits

Emma earns $6 each time she mows the lawn and $8 per hour for babysitting i.e. $6x+8y$