Question

A manufacturer of nickel-hydrogen batteries randomly selected 100 nickel plates for test cells, cycled them a specified number of times, and determined that 14 of the plates have blistered. 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. Please use a full 4-part hypothesis test: Hypotheses, check assumptions, calculations and conclusion. Please show your R code that gives you your p-value

Answer 1

Code:

x <- 14
n <- 100
p <- x/n
po <- .10

z <- (p-po)/sqrt(po*(1-po)/n)
z

1-pnorm(z,0,1)

Analysis:

part 1: Assumptions:

for application of normal approximation to binomial, np >= 5 and nq >= 5

In this case, np = 100*.14 = 14 and nq = 100*(1-0.14) = 86. hence normal approximation to binomial is valid.

Part 2: Hypothesis:

Ho: p = 10%; 10% of all plates blister.
h1: p > 10%; more than 10% of all plates blister.

Part 3: calculations

Part 4: conclusion

With z = 1.33, p>5%, i fail to reject ho and conclude that p = 10%

there is no sufficient evidence to conclude that more than 10% of all plates blister.