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bezimeni [28]
3 years ago
13

A simple random sample of 85 students is taken from a large university on the West Coast to estimate the proportion of students

whose parents bought a car for them when they left for college. When interviewed, 51 students in the sample responded that their parents bought them a car. What is a 95% confidence interval for p, the population proportion of students whose parents bought a car for them when they left for college
Mathematics
1 answer:
ahrayia [7]3 years ago
6 0

Answer:

95% confidence interval for p, the population proportion of students whose parents bought a car for them when they left for college

(0.4958 , 0.7041)

Step-by-step explanation:

<u><em>Step(i):-</em></u>

Given that the sample size 'n' = 85

The sample proportion

            p = \frac{x}{n} = \frac{51}{85} = 0.6

95% confidence interval for p, the population proportion of students whose parents bought a car for them when they left for college

(p^{-} -Z_{0.05} \sqrt{\frac{p(1-p)}{n} } , p^{-} +Z_{0.05} \sqrt{\frac{p(1-p)}{n} })

<u><em>Step(ii):-</em></u>

Given that the level of significance

α = 0.05

Z₀.₀₅ = 1.96

(0.6 -1.96 \sqrt{\frac{06(1-06)}{85} } , 0.6 +1.96 \sqrt{\frac{0.6(1-0.6)}{85} })

(0.6 - 0.104138 , 0.6 +0.104138)

(0.4958 , 0.7041)

<u><em>Final answer:-</em></u>

95% confidence interval for p, the population proportion of students whose parents bought a car for them when they left for college

(0.4958 , 0.7041)

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Using a system of equation, we have that:

a)

  • x, which is the cost of on-site service.
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b)

The system is:

x = 3y

z = y - 10

15x + 40y + 5z = 3100

c)

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Item a:

The variables are:

  • x, which is the cost of on-site service.
  • y, which is the cost of at-store service.
  • z, which is the cost of by-mail service.

Item b:

On-site service costs <u>3 times as much as at-store service</u>, thus:

x = 3y

By mail service costs <u>$10 less than at-store</u>  service, thus:

z = y - 10

Last week, the shop completed <u>15 services on-site, 40 services at-store, and 5 services by mail for total sales of $3100</u>, thus:

15x + 40y + 5z = 3100

The system is:

x = 3y

z = y - 10

15x + 40y + 5z = 3100

Item c:

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15x + 40y + 5z = 3100

15(4y) + 40y + 5(y - 10) = 3100

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105y = 3150

y = \frac{3150}{105}

y = 30

Then

x = 3y = 3(30) = 90

The cost of one on-site repair service is of $90.

A similar problem is given at brainly.com/question/24823220

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