Question

In: Statistics and Probability

A sample of 1100 computer chips revealed that 58% of the chips fail in the first...

A sample of 1100 computer chips revealed that 58% of the chips fail in the first 1000 hours of their use. The company's promotional literature claimed that less than 61% fail in the first 1000 hours of their use. Is there sufficient evidence at the 0.01 level to support the company's claim?

State the null and alternative hypotheses for the above scenario.

Solutions

Expert Solution

Solution:

Here, we have to use one sample z test for the population proportion.

The null and alternative hypotheses for this test are given as below:

Null hypothesis: H0: About 61% fail in the first 1000 hours of their use.

Alternative hypothesis: Ha: Less than 61% fail in the first 1000 hours of their use.

H0: p = 0.61 versus Ha: p < 0.61

This is a lower tailed test.

We are given

Level of significance = α = 0.01

Test statistic formula for this test is given as below:

Z = (p̂ - p)/sqrt(pq/n)

Where, p̂ = Sample proportion, p is population proportion, q = 1 - p, and n is sample size

n = sample size = 1100

p̂ = x/n = 0.58

p = 0.61

q = 1 - p = 0.39

Z = (p̂ - p)/sqrt(pq/n)

Z = (0.58 - 0.61)/sqrt(0.61*0.39/1100)

Z = -2.0400

Test statistic = -2.0400

P-value = 0.0207

(by using z-table)

P-value > α = 0.01

So, we do not reject the null hypothesis

There is not sufficient evidence to conclude that Less than 61% fail in the first 1000 hours of their use.


Related Solutions

A sample of 1100 computer chips revealed that 48% of the chips fail in the first...
A sample of 1100 computer chips revealed that 48% of the chips fail in the first 1000 hours of their use. The company's promotional literature states that 51% of the chips fail in the first 1000 hours of their use. Is there a sufficient evidence at the 0.05 level to support the companies claim? state the null and alternative hypothesis for the above scenarios? H0= Ha=
26. A sample of 1100 computer chips revealed that 62% of the chips fail in the...
26. A sample of 1100 computer chips revealed that 62% of the chips fail in the first 1000 hours of their use. The company's promotional literature states that 60% of the chips fail in the first 1000 hours of their use. The quality control manager wants to test the claim that the actual percentage that fail is different from the stated percentage. State the null and alternative hypotheses. H0: Ha: 27. A sample of 1100 computer chips revealed that 62%...
A sample of 900 computer chips revealed that 59% of the chips fail in the first...
A sample of 900 computer chips revealed that 59% of the chips fail in the first 1000 hours of their use. The company's promotional literature states that 62% of the chips fail in the first 1000 hours of their use. The quality control manager wants to test the claim that the actual percentage that fail is less than the stated percentage. Is there enough evidence at the 0.10 level to support the manager's claim? Step 2 of 7: Find the...
A sample of 900 computer chips revealed that 59% of the chips fail in the first...
A sample of 900 computer chips revealed that 59% of the chips fail in the first 1000 hours of their use. The company's promotional literature states that 62% of the chips fail in the first 1000 hours of their use. The quality control manager wants to test the claim that the actual percentage that fail is less than the stated percentage. Is there enough evidence at the 0.10 level to support the manager's claim? Step 2 of 7: Find the...
A sample of 800 computer chips revealed that 59% of the chips fail in the first...
A sample of 800 computer chips revealed that 59% of the chips fail in the first 1000 hours of their use. The company's promotional literature claimed that 63% fail in the first 1000 hours of their use. Is there sufficient evidence at the 0.01 level to dispute the company's claim? State the null and alternative hypotheses for the above scenario.
A sample of 1200 computer chips revealed that 72% of the chips fail in the first...
A sample of 1200 computer chips revealed that 72% of the chips fail in the first 1000 hours of their use. The company's promotional literature claimed that below 75% fail in the first 1000 hours of their use. Is there sufficient evidence at the 0.02 level to support the company's claim? State the null and alternative hypotheses for the above scenario.
A sample of 1600 computer chips revealed that 47% of the chips fail in the first...
A sample of 1600 computer chips revealed that 47% of the chips fail in the first 1000 hours of their use. The company's promotional literature states that 44% of the chips fail in the first 1000 hours of their use. The quality control manager wants to test the claim that the actual percentage that fail is different from the stated percentage. Is there enough evidence at the 0.01 level to support the manager's claim?
A sample of 16001600 computer chips revealed that 21%21% of the chips fail in the first...
A sample of 16001600 computer chips revealed that 21%21% of the chips fail in the first 10001000 hours of their use. The company's promotional literature states that 23%23% of the chips fail in the first 10001000 hours of their use. The quality control manager wants to test the claim that the actual percentage that fail is different from the stated percentage. Is there enough evidence at the 0.020.02 level to support the manager's claim? signifigant evidence or not enough evidence
A sample of 800 computer chips revealed that 75% of the chips do not fail in...
A sample of 800 computer chips revealed that 75% of the chips do not fail in the first 1000 hours of their use. The company's promotional literature claimed that more than 72% do not fail in the first 1000 hours of their use. Is there sufficient evidence at the 0.01 level to support the company's claim? Step 1 of 1: State the null and alternative hypotheses for the above scenario.
A sample of 1300 computer chips revealed that 42% of the chips do not fail in...
A sample of 1300 computer chips revealed that 42% of the chips do not fail in the first 10001000 hours of their use. The company's promotional literature claimed that above 39% do not fail in the first 1000hours of their use. Is there sufficient evidence at the 0.05 level to support the company's claim? State the null and alternative hypotheses for the above scenario. Step 1 of 3: Find the point estimate for the true difference between the population means....
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT