Question

Harry Potter ~ Many people love reading books like Harry Potter. Historically, it has been estimated that the proportion of book readers, who like to read fiction, is 0.482. Camille is a Harry Potter fan and a fan of fiction books. She wants to determine if the actual proportion of book readers who like to read fiction is different from the historical value. From a recent survey of randomly selected 14,991 book readers, she learns that 7,014 like to read fiction.

A normal distribution is used to carry out the following hypothesis test:

HO: P= .482 vs HA : P =/.482

What is the test statistic for this hypothesis test? Give your answer to 4 decimal places.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H0 : p =0.482

Ha : p 0.482

n =14,991

x =7,014

= x / n =7014 / 14991=0.468

P0 = 0.482

1 - P0 = 1 - 0.482 = 0.518

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

= 0.468 - 0.482 / [0.482* 0.518 / 14,991 ]

= -3.48

Test statistic = z =-3.48

P(z < -3.48) = 0.0003

P-value = 2 * 0.0003 = 0.0006