Question

The manufacturer of aspirin claims that the proportion of headache suffers who get relief with just two aspirins is 53%. The probability is 90% that the sample percentage (for a sample of 400) will be contained within what symmetrical limits of the population percentage?

Answer 1

Solution

Given that,

p = 53% = 0.53

1 - p = 1 - 0.53 = 0.47

n = 400

= p = 0.53

=  [p( 1 - p ) / n] = [(0.53 * 0.47) / 400] = 0.0250

Using standard normal table,

P( -z < Z < z) = 90%

= P(Z < z) - P(Z <-z ) = 0.90

= 2P(Z < z) - 1 = 0.90

= 2P(Z < z) = 1 + 0.90

= P(Z < z) = 1.90 / 2

= P(Z < z) = 0.95

= P(Z < 1.645) = 0.95

= z  ± 1.465

Using z-score formula,

  = z *   +  

  = -1.645 * 0.0250 + 0.53

  = 0.489

  = 48.9%

Using z-score formula,

  = z *   +  

  = 1.645 * 0.0250 + 0.53

  = 0.571

  = 57.1%

The probability is 90% that the sample percentage will be contained above 48.9% and below 57.1%