Question

You are conducting a study to see if the probability of catching the flu this year is significantly less than 0.73. You use a significance level of α=0.001α=0.001.

      H0:p=0.73H0:p=0.73
      H1:p<0.73H1:p<0.73

You obtain a sample of size n=481n=481 in which there are 339 successes.

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H₀ : p = 0.73

H_a : p < 0.73

= x / n = 339 / 481 = 0.705

P₀ = 0.73

1 - P₀ = 1 - 0.73 = 0.27

Test statistic = z =

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.705 - 0.73 / [(0.73 * 0.27) / 481 ]

Test statistic = z = 0.0202428086 -1.235

P(z < -1.235)

P-value = 0.1084