The manufacturer of the ColorSmart-5000 television set claims 95 percent of its

Question

The manufacturer of the ColorSmart-5000 television set claims 95 percent of its sets last at least five years without needing a single repair, In order to test this claim, a consumer group randomly selects 378 consumers who have owned a ColorSmart-5000 television set for five years. Of these 378 consumers, 321 say their ColorSmart-5000 television sets did not need a repair, whereas 57 say their ColorSmart-5000 television sets did need at least one repair Determine the sample size needed in order to be 90 percent confident that p, the sample proportion of ColorSmart-5000 television sets that last at least five years without a single repair wdhn a margin of error of 03 of p, the population proporton of sets that last at least five years without a single repair (Round your p answer to 5 decimal places Round your n answer to the next whole number) and 2 oon 2576

Explanation / Answer

We have to find the value of sample size n, but first we need to determine the proportion given in the question in order to solve for the sample size n
Proportion = (321/378) = 0.84921
Now, we will use the following formula to solve for the required sample size
n = (p*q)(z/ME)^2
where p = 0.84921, q = 1-0.84921 = 0.15079, z = 2.576 and Margin of error ME = 0.03
setting the given values in the above formula, we get
sample size(n) = (0.84921*0.15079)*(2.576/0.03)^2= 944.14 which is rounded off to nearest whole number
so answer is n = 944

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

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