Question

g A manufacturer of nickel-hydrogen batteries randomly selects 100 nickel plates for test cells, cycles them a specified number of times, and determines that 11 of the plates have blistered. Does this provide compelling evidence for concluding that more than 10% of all plates blister under such circumstances

Answer 1

Complete Question

A manufacturer of nickel-hydrogen batteries randomly selects 100 nickel plates for test cells, cycles them a specified number of times, and determines that 11 of the plates have blistered. Does this provide compelling evidence for concluding that more than 10% of plates blister under such circumstances?

A) State H_0 and H_a, (5 pts)

B) Test the hypothesis using the P-Value approach at a significance level of 4%: (15 pts)

Expert Answer

Answer:

a)
`H_0:p=0.10`

`H_a:p>0.10`

b) We fail to reject Null hypothesis

Explanation:

From the question we are told that:

Sample size n=100

No. with blistered x=11

a)

Generally the Hypothesis given as

`H_0:p=0.10`

`H_a:p>0.10`

b)

Since p=0.10

Therefore

`p'=(11)/(100)`

`p'=0.11`

Test statistics

`Z=(p'-p)/(√(p(1-p)))`

`Z=(0.11-0.10)/(√(0.10*0.90/100))`

`Z=1.33`

From table

`P-Value =0.092`

Therefore

P-value >0.04 significance level

Hence,We cannot conclude that at
`4\%` significance level the proportion is greater than
`10\%`

We fail to reject Null hypothesis