Amanufacturer of nickel-hydrogen batteries randomly selects 100 nickel plates for test cells, cycles them a specified number of times, and determines that 14 of the plates have blistered.

(a) does this provide compelling evidence for concluding that more than 10% of all plates blister under such circumstances? state and test the appropriate hypotheses using a significance level of .05. in reaching your conclusion, what type of error might you have committed?

(b) if it is really the case that 15% of all plates blister under these circumstances and a sample size 100 is used, how likely is it that the null hypothesis of part (a) will not be rejected by the 0.05 test? answer this question for a sample size of 200.

(c) how many plates would have to be tested to have \(\beta(.15)\) = 0.10 for the test of part (a)?

Step-by-step explanation:

Test the claim about a single population proportion where the null hypothesis is of the form of {H_0}:p = {p_0}H  

The formula for single proportion is,

Here, pp denote the population proportion

Let be the number of successes in a sample of size.

Let be the total sample size.

a)

Null hypothesis,

Alternative hypothesis,

Level of significance,

Decision Rule: Reject

Calculate the test statistic value.

Calculate the p−value of the test.

(b)

It is really case that 15% of all plates blister under these circumstances and a sample size of 100 is used.

Hence, the probability that will not be rejecting using the  is 0.4927.

Therefore, there is 49.27% of all samples will result in correct rejection of null hypothesis

For the sample size n = 200,n=200, the probability of type-II error is calculated as follows:

(c)

The number of plates is,

600,000,000,000, or 6e14

step-by-step explanation:

8/k

step-by-step explanation: