Question

Last year, 10 percent of all teenagers purchased a new iPhone. This year, a sample of 260 randomly chosen teenagers showed that 39 had purchased a new iPhone. To test whether the percentage has risen, the p-value is approximately:

the answer is 0.0070 Please explain. Im studying for a test.

Answer 1

Sol:

Null hypothesis:

Ho:p=0.10

Alternative hypothesis

To test whether the percentage has risen so

Ha:p>0.10

alpha=0.05 as nothing is specified about significance level

Test statistic

Z=p^-p/sqrt(p*(1-p)/n)

p^=x/n=39/260=0.15

p=10%=0.10

n=260

z=0.15-0.10/sqrt(0.10*(1-0.10)/260)

z=2.687419

Need to find p

P(Z>2.687)

so

1-left tail probbaility

=1-P(>2.687)

=1-{=NORM.S.DIST(2.687419,TRUE)}

=1-0.9964

=0.0036

p=0.0036

p value to be 0.0036

P<0.05

Reject Ho.
Accept Ha.

There is sufficient evidence to support the claim that

the percentage has risen,

But if you do binom.test in R software

Just give below command in R studio

binom.test(39,260,p=0.10,alternative="greater")

Output:

data: 39 out of 260
number of successes = 39, number of trials = 260,
p-value = 0.007029
alternative hypothesis: true probability of success is greater than 0.1
95 percent confidence interval:
0.1147804 1.0000000
sample estimates:
probability of success
0.15

FROM HERE

p-value = 0.007029 which is answer given