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Pani-rosa
10 days ago
7

400 students were randomly sampled from a large university, and 289 said they did not get enough sleep. Conduct a hypothesis tes

t to check whether this represents a statistically significant difference from 50%, and use a significance level of 0.01.
Mathematics
1 answer:
babunello [3.6K]10 days ago
3 0

Answer:

The sample proportion shows a statistically significant divergence from 50%

Step-by-step explanation:

Null hypothesis: The sample proportion equals 50%

Alternative hypothesis: The sample proportion does not equal 50%

z = (p' - p) ÷ sqrt[p(1 - p) ÷ n]

p' is the sample proportion = 289/400 = 0.7225

p is the population proportion = 50% = 0.5

n is the number of students surveyed = 400

z = (0.7225 - 0.5) ÷ sqrt[0.5(1 - 0.5) ÷ 400] = 0.2225 ÷ 0.025 = 8.9

The analysis is two-tailed. At a significance level of 0.01, the critical value is 2.576. The acceptance region for the null hypothesis is between -2.576 and 2.576.

Conclusion:

Reject the null hypothesis since the calculated z-score of 8.9 is beyond the bounds established by the critical values of -2.576 and 2.576.

There is compelling evidence to support the assertion that the sample proportion signifies a meaningful difference from 50%.

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I think it’s 156 hundreds, 3 tens, and 8 ones.
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Jacque needs to buy some pizzas for a party at her office. She's ordering from a restaurant that charges a \$7.50$7.50dollar sig
Svet_ta [4296]

Answer:

Step-by-step explanation:

Delivery charge = $7.50

Cost per pizza = $14

Budgeted total = $60

7.50 + 14p < 60

First, subtract 7.50 from both sides

14p < 60 - 7.50

14p < 52.50

Now divide both sides by 14

p < 52.50 / 14

p < 3.75

Each pizza consists of 8 slices

Therefore, the total number of slices she can buy = 3.75 × 8

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17 days ago
Chiang is filling a 50ft container with water at a rate of 0.5 ft/ min. interpret the key features for this situation
Leona [4145]

Answer:

The main aspects are

50ft³ = volume

0.5ft³/min = filling rate

Time= 100 minutes

Step-by-step breakdown:

Chiang is in the process of filling a 50ft container with water at a speed of 0.5 ft/min.

50ft³ = volume

0.5ft³/min = flow rate

It’s important to note that we still need to determine how long it will take to fill the 50 ft³ container.

Time = volume / rate

Time = 50 ft³ / 0.5 ft³/min

Time = 50 / 0.5 min

Time = 100 min

The main aspects are

50ft³ = volume

0.5ft³/min = filling rate

Time= 100 minutes

7 0
13 days ago
Nico owns 11 instructional piano books. Two are beginner books, six are intermediate books, and three are advanced books. If two
PIT_PIT [3895]
There are 2 beginner, 6 intermediate, and 3 advanced books, totaling 11.

P(advanced) = 3/11
replaced
P(beginner) = 2/11

P(both) = 3/11 * 2/11 = 6/121 <=
8 0
3 days ago
A solid oblique cone with a slant length of 17 units is placed inside an empty cylinder with a congruent base of radius 8 units
PIT_PIT [3895]

Step 1

Calculate the volume of a cylinder

We understand that

the volume of a cylinder can be expressed as

V1=\pi r^{2} h

In this scenario

r=8\ units \\ h=15\ units

Insert the values

V1=\pi 8^{2} 15

V1=960\pi\ units^{3}

Step 2

Calculate the volume of a cone

We are aware that

the volume of a cone equals

V2=\frac{1}{3}\pi r^{2} h

In this example

r=8\ units \\ l=17\ units \\ h=?

Use the Pythagorean Theorem to determine the height h

h^{2} =l^{2}-r^{2}\\ h^{2} =17^{2}-8^{2}\\ h^{2}=225\\ h=15\ units

V2=\frac{1}{3}\pi 8^{2} 15\\ \\ V2=320\pi \ units^{3}

Step 3

Calculate the empty volume inside the cylinder

V1-V2=960\pi -320\pi =640\pi \ units^{3}

Thus

the final result is

the empty volume inside the cylinder is 640\pi \ units^{3}

6 0
8 days ago
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