Question

On the basis of past history, a car manufacturer knows that 10% (p = .10) of all newly made cars have an initial defect. In a random sample of n = 100 recently made cars, 13%

(p^=.13)(\hat{p} = .13)

have defects. Find the value of the standardized statistic (z-score) for this sample proportion.

Solution

Verified
Step 1
1 of 2

We will use the formula for the zz-score for a sample proportion:

z=p^pp(1p)n,z=\frac{\hat p - p}{\sqrt{\frac{p\cdot(1-p)}{n}}} ,

where pp is the population proportion, nn is the sample size and p^\hat p is the value of sample statistic (proportion).

Inserting the values p=0.1p=0.1 (10%10\% of all\textbf{all} newly made cars have an initial defect, so this is the population parameter), n=100n=100 (a sample of 100 newly made cars was taken), and p^=0.13\hat p=0.13 (13%13\% of cars from the sample\textbf{from the sample} had defects) into the formula above yields the value of zz-score for a sample proportion:

z=0.130.10.10.9100=1.\boxed{z}=\frac{0.13-0.1}{\sqrt{\frac{0.1\cdot0.9}{100}}}=\boxed{1} .

Create an account to view solutions

Create an account to view solutions

Recommended textbook solutions

Calculus: Early Transcendentals 8th Edition by James Stewart

Calculus: Early Transcendentals

8th EditionISBN: 9781285741550 (4 more)James Stewart
11,083 solutions
Mind on Statistics 5th Edition by Jessica M. Utts, Robert F. Heckard

Mind on Statistics

5th EditionISBN: 9781285974576Jessica M. Utts, Robert F. Heckard
1,617 solutions
Calculus: Early Transcendentals 9th Edition by Daniel K. Clegg, James Stewart, Saleem Watson

Calculus: Early Transcendentals

9th EditionISBN: 9781337613927 (2 more)Daniel K. Clegg, James Stewart, Saleem Watson
11,047 solutions
The Practice of Statistics for the AP Exam 5th Edition by Daniel S. Yates, Daren S. Starnes, David Moore, Josh Tabor

The Practice of Statistics for the AP Exam

5th EditionISBN: 9781464108730 (2 more)Daniel S. Yates, Daren S. Starnes, David Moore, Josh Tabor
2,433 solutions

More related questions

1/4

1/7