can some one help me solve 9,10 in order to insure the estimate is accurate with

Question

can some one help me solve 9,10

in order to insure the estimate is accurate within 4% of the population proportion. A tea drinker's society estimates that the mean consumption of tea by a person in the US is more than 8 gallons per year. In a random sample of 100 people, you find that the mean consumption of tea is 7.9 gallons per year with a standard deviation of 2.67 gallons. At alpha = .07 can you support the society's claim? A computer repairer believes that the mean repair cost for damaged computers is more than $95. To test this claim, you determine the repair costs for 7 randomly selected computers and find that the mean repair cost is $100 per computer with a standard deviation of $42.50. At alpha = .01, do you have enough evidence to support the repairer's claim? A research centre estimates that at least 20% of US adults are smokers. In a random sample of 200 adults, 18.5% say that they are smokers. At alpha = .01, is there enough evidence to reject the claim? The mean repair cost for 34 Model A ovens is $50 with a standard deviation of$10, and the mean repair cost for 46 Model B ovens is $60 with a standard deviation of $18. At a significance level of 0.01 can you reject the claim that repair costs for these two models are the same? The mean repair cost for 14 randomly selected small cars is $473 with a standard deviation of$190 and the mean repair cost for 23 midsize cars is $741 with a standard deviation of $205. At a significance level of 0.10, and assuming that the population variances are equal, can you conclude that repair cost is less for small cars than it is for midsize cars? A random sample of 19 residents of County A has a mean annual income of $45, 200 and a standard deviation of $9, 300. A random sample of 15 residents of County B has a mean annual income of $40, 700 and a standard deviation of $5, 500. At a significance level of 0.10, and assuming that the population variances are not equal, can you conclude that mean income in County A greater than the mean income in County B?

Explanation / Answer

Q9.

Given that,
mean(x)=473
standard deviation , s.d1=190
number(n1)=14
y(mean)=741
standard deviation, s.d2 =205
number(n2)=23
null, Ho: u1 > u2
alternate, H1: u1 < u2
level of significance, = 0.1
from standard normal table,left tailed t /2 =1.306
since our test is left-tailed
reject Ho, if to < -1.306
calculate pooled variance s^2= (n1-1*s1^2 + n2-1*s2^2 )/(n1+n2-2)
s^2 = (13*36100 + 22*42025) / (37- 2 )
s^2 = 39824.2857
we use test statistic (t) = (x-y)/sqrt(s^2(1/n1+1/n2))
to=473-741/sqrt((39824.2857( 1 /14+ 1/23 ))
to=-268/67.6467
to=-3.9618
| to | =3.9618
critical value
the value of |t | with (n1+n2-2) i.e 35 d.f is 1.306
we got |to| = 3.9618 & | t | = 1.306
make decision
hence value of | to | > | t | and here we reject Ho
p-value: left tail - ha : ( p < -3.9618 ) = 0.00017
hence value of p0.1 > 0.00017,here we reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate,conclude that repair cost is less for small cars, H1: u1 < u2
test statistic: -3.9618
critical value: -1.306
decision: reject Ho
p-value: 0.00017

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.