Dark mode

Interval estimates for proportions — Question 320

Original QCE Vault practice · 3 marks

Q320 · Practice questionTechnology-freeComplex familiar3 marks

QUESTION 320 (3 marks)

A

95\%

approximate confidence interval has unrounded endpoints

0.45

and

0.55

. The construction used

\widehat p=0.5

and

z=2

as a convenient approximation.

a)

Determine the sample size used.

[2 marks]

b)

Determine the number of successes in the sample.

[1 mark]

Question linkSyllabus coverage

Related questions

Q10 · Original practice · 1 mark
A sample has $\hat p=0.40$ and $n=100$ . Using $z=1.96$ , the approximate margin of error for a 95% confidence interval is
Interval estimates for proportions
Q20 · Original practice · 1 mark
A sample of 625 gives $\hat p=0.52$ . A 95% confidence interval using $z=1.96$ is closest to
Interval estimates for proportions
Q35 · Original practice · 3 marks
A random sample of 400 gives $\hat p=0.48$ . Using $z=1.96$ , determine an approximate 95% confidence interval for the population proportion.
Interval estimates for proportions
Q45 · Original practice · 4 marks
A pilot study estimates a population proportion as $0.37$ . Determine the minimum sample size required so that an approximate 95% confidence interval has margin of error at most $0.03$ , using the pilot estimate in the calculation.
Interval estimates for proportions