Cost of Health Care ~ Have you or a member of your immediate family put off medical treatment due to cost during the past year? In 2016, a survey asked 967 randomly selected American adults this question and 184 said yes. In 2019, another survey asked the same question to 1015 randomly selected American adults and 253 said yes. We want to determine if there is a difference between the proportion of Year 2016 American adults and Year 2019 American adults, who put off medical treatment due to cost.

1) There must be at least 10 observed successes and 10 observed failures in the sample from population 1.

3) There must be at least 10 observed successes and 10 observed failures in the sample from population 2.

Step-by-step explanation:

Hello!

You have two variables of interest:

X₁: Number of that had to put off medical treatment due to cost during 2016.

n₁= 967 people surveyed

sample proportion p'₁= 184/967= 0.19

X₂: Number of that had to put off medical treatment due to cost during 2019.

n₂= 1015 people surveyed

p'₂= 253/1015= 0.25

The pooled sample proportion is

To study the population proportion you have to apply the Central Limit Theorem to approximate the distribution of the sample proportion to normal, the conditions for a valid approximation are:

Sample size n ≥ 30

n₁= 967

n₂= 1015

n*p'≥10 (each sample contains at least 10 successes)

n₁*p'₁= 967*0.19= 183.73

n₂*p'₂= 1015*0.25= 253.75

n*(1-p')≥10 (each sample contains at least 10 failures)

n₁*(1-p'₁)= 967*0.81= 783.27

n₂*(1-p'₂)= 1015*0.75= 761.25

1) There must be at least 10 observed successes and 10 observed failures in the sample from population 1.

3) There must be at least 10 observed successes and 10 observed failures in the sample from population 2.

I hope it helps!

Related Questions

A math student has a plan to solve the following system by the elimination method. to eliminate the x-term , he wants to multiply the top equation by 7. what should he multiply the second equation by so that when he adds the equation, the x-term are eliminated ? -3x-7y=-56-7x+10y=-1

9514 1404 393

-3

Step-by-step explanation:

The coefficients of the x-terms are (-3, -7). If you swap them, you have (-7, -3). Negating one of them will give you (7, -3) or (-7, 3). Either of these pairs of multipliers will work to eliminate the x-terms.

The problem statement tells us the multiplier of the first equation is 7, so the multiplier of the second equation needs to be -3.

A restaurant in a fast food franchise has determined that the chance a customer will order a soft drink is 0.88. The probability that a customer will order a hamburger is 0.53.
The probability that a customer will order french fries is 0.49.
Complete parts a and b below.
a. If a customer places an order, what is the probability that the order will include a soft drink and no fries, if these two events are independent? (Round to four decimal places as needed.)
The probability is____________.
b. The restaurant has also determined that, if a customer orders a hamburger, the probability the customer will order fries is 0.71.
Determine the probability that the order will include a hamburger and fries. (Round to four decimal places as needed.)
The probability is________

A) P(soft drink, hamburger, no fries) = 0.1912

B) P(fries and hamburger) = 0.3763

Step-by-step explanation:

A) Probability that the order will include a soft drink, a hamburger and no fries is;

P(soft drink, hamburger, no fries) = P(soft drink) x P(hamburger) x P(no French fries)

P(soft drink, hamburger, no fries) = 0.88 x 0.53 x (1 - 0.49) = 0.88 × 0.53 × 0.41 ≈ 0.1912

B) we are told that;

P(fries|hamburger)=0.71

Since P(fries|hamburger) = P(fries and hamburger)/P(hamburger)

Thus;

0.71 = P(fries and hamburger)/0.53

P(fries and hamburger)= 0.71 *0.53

P(fries and hamburger) = 0.3763

Question a's answer is 0.4488 meaning there's a 44.88% chance a customer will order a soft drink and no fries. For question b, the answer is 0.3763 meaning there's a 37.63% chance that an order will include a hamburger and fries.

Explanation:

To calculate probabilities of independent events, you simply multiply the probability of each event happening.

For question a. the probability of ordering a soft drink is given as 0.88, and the probability of ordering fries is given as 0.49. However, we want the probability of ordering a soft drink and not ordering fries, which means we need to take the complement of the fries event (1-0.49) which is 0.51. Multiply the probability of ordering a soft drink (0.88) with the probability of not ordering fries (0.51):

0.88 x 0.51 = 0.4488

Therefore the probability of a customer ordering a soft drink and no fries is 0.4488.

For question b. we are given the conditional probability that a customer will order fries given they have already ordered a hamburger, which is 0.71. To calculate the joint probability of both events (hamburger and fries), we must multiply the conditional probability by the probability of the hamburger event:

0.71 x 0.53 = 0.3763

Therefore the probability of an order including a hamburger and fries is 0.3763.

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A 46- inch piece of steel is cut into three pieces so that the second piece is twice as long ad the first piece , and the third piece is one inch more than six times the length of the first piece. Find the lengths of the pieces.

Hope this helps you.

The first piece is 5 inches long, the second piece is 10 inches long, and the third piece is 31 inches long.

Explanation:

The problem involves a piece of steel that is 46 inches long and it is cut into three pieces. The wording of the problem gives us equations we can use to solve for lengths of the pieces. We're told:

• The second piece is twice as long as the first piece.
• The third piece is one inch more than six times the length of the first piece.

We can let x represent the length of the first piece. Then the length of the second piece is 2x, and the length of the third piece is 6x+1.

Because the three pieces together form the original 46-inch piece, we can set up this equation: x + 2x + 6x + 1 = 46, which simplify to 9x +1 = 46. Solving for x gives x = 5. Therefore, the lengths of the pieces are 5 inches, 10 inches (2 * 5), and 31 inches (6 * 5 + 1).

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One cell phone company offers a plan that costs $25.99 and includes unlimited night and weekendminutes. Another company offers a plan that costs$14.99 and charges \$0.35 per minute during nights
and weekends. For what numbers of night and weekend minutes does the second company's plan cost
more than the first company's plan?

25

Step-by-step explanation:

15. In the State of California, there are 25 full-time employees to every 4 part-time employees. If there are 250,000 full-time employees, how many part-time employees are there statewide?

40,000
I know it's not the mathematical way, but it's the same ratio, so just add the same amount of zeroes.

To find the number of part-time employees in California, set up a proportion and solve for x.

Explanation:

To find the number of part-time employees statewide, we can set up a proportion using the given information. We know that there are 25 full-time employees for every 4 part-time employees. So, we can write the proportion as:

25 full-time employees / 4 part-time employees = 250,000 full-time employees / x part-time employees

Cross-multiplying, we get:

25x = 4 * 250,000

Simplifying, we have:

25x = 1,000,000

Dividing both sides by 25, we find:

x = 40,000

Therefore, there are 40,000 part-time employees statewide in California.

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A Cepheid variable star is a star whose brightness alternately increases and decreases. For a certain star, the interval between times of maximum brightness is 4.2 days. The average brightness of this star is 3.0 and its brightness changes by ±0.25. In view of these data, the brightness of the star at time t, where t is measured in days, has been modeled by the function B(t) = 3.0 + 0.25 sin 2πt 4.2 . (a) Find the rate of change of the brightness after t days. dB dt =