Question

In a sample of 143 bears, 50 were female. Use this information and Excel to undertake a hypothesis test to determine whether one third of the bears in a particular population are female. Use the output to answer the following questions.

1. What is the value of p?  (2 dp)
2. What is the value of p-hat?  (2 dp)
3. What is the absolute value of the test statistic [Hint: don't round p or p-hat in your calculation]?  (2dp)
4. What is the p-value? (3 dp)
5. Would you (A) reject or (B) not reject the null hypothesis?
6. Is it reasonable to conclude that the proportion of female bears is significantly different to one third? (Y) or (N)

Answer 1

null Hypothesis: Ho: alternate Hypothesis: Ha: 0.333 0.333 1.960 for 0.05 level with two tailed test, critical value of z= Decision rule: reject Ho if absolute value of test statistic 1z|>1.96 50 sample success sample size 143.0 std error =Se = (p*(1-p)/n) = 0.0394 sample proportion p x/n= 0.3497 test stat = z (0-p)/Se= 0.41 p value 0.6789

value of p =1/3=0.3333

value of p-hat =50/143 =0.3497

absolute value of the test statistic =0.41

p value =0.679

not reject the null hypothesis

(N)