Question

9% of all Americans suffer from sleep apnea. A researcher suspects that a lower percentage of those who live in the inner city have sleep apnea. Of the 382 people from the inner city surveyed, 23 of them suffered from sleep apnea. What can be concluded at the level of significance of αα = 0.10?

1. For this study, we should use Select an answer z-test for a population proportion t-test for a population mean
2. The null and alternative hypotheses would be:
   Ho: ? μ p  ? = ≠ < >   (please enter a decimal)   
   H₁: ? μ p  ? ≠ = < >   (Please enter a decimal)

3. The test statistic ? t z  =  (please show your answer to 3 decimal places.)
4. The p-value =  (Please show your answer to 4 decimal places.)
5. The p-value is ? ≤ >  αα
6. Based on this, we should Select an answer fail to reject accept reject  the null hypothesis.

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H₀ : p = 0.09

H_a : p < 0.09

= x / n = 23 / 382 = 0.0602

P₀ = 0.09

1 - P₀ = 0.91

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.0602 - 0.09 / [(0.09 * 0.91) / 382]

= -2.035

P(z < -2.035) = 0.0209

P-value = 0.0209

= 0.10

P-value <

Reject the null hypothesis .