Question

A manufacturer of nickel-hydrogen batteries randomly selects 120 nickel plates for test cells, cycles them a specified number of times, and determines that 19 of the plates have blistered. a. Does this provide compelling evidence for concluding that more than 12% of all plates blister under such circumstances? State and test the appropriate hypotheses using a significance level of .05. b. If it is really the case that 17% of all plates blister under these circumstances and a sample size of 100 is used, how likely is it that the null hypothesis of part (a) will not be rejected by the level .05 test?.

Answer 1

b.) Not rejecing the hypothesis when it false is type 2 error

P(Do not reject | P=0.17)

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To calculate this probability first we find the range of proportion when we will not reject

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In our case it is p<0.173

Then we write

P(p<0.173| P=0.17)

To calculate probability we standardize this p by using the given P=0.17

Then see the standard normal table to know the probability.
Decision since it is observed that not the Zo 1.284 < 2.c = 1.04 it is then concluded that thero sull Hypothesis is not rejected. Conclusion It is concluded that the Null hypothesis to is not rejected. Therefore there is enough evidence to claim that the population proportion is greater tham 0.12 at x=0.05 level of significance. Girew, by Ione Proportion P=0.17 Sample sine na 100 critical value at a=0ios at radioss 1.64 Piere for we will not reject Ho ý Z < 1.64 þ-P <1-64 JPA $ 0.12 < 1.64 Q dies 0:12X0.88 00 ♡ $3.0:12 F070533 p < 0.173 Do not reject to Now p (Do not siejee t. Ho | P=0:17) = P(p<0-173) P=0:17) P (22 0'17* z < 0173-0.17 01720183 7: Z = t=P_2 POS s 2

070376 (). 0:03 1:04 . P(Z < 0.003 P(z Z < 0.0*797) = PEZZ0.08) = 0.5+ POLZ 20.08) t 0.0319 = 0.5319 which is the required probablloty. zo