Question

It is believed that 11% of all Americans are left-handed. A college needs to know how many left-handed desks to place in the big lecture halls being constructed on its campus. In a random sample of 200 students from that college, 30 were left-handed. Does this provide enough evidence to show that students at this college have a higher percentage of left-handers than the general American population? Set up the hypotheses.

a.) Fill in the correct null and alternative hypotheses:

H0:H0: ? μ N σ s X n p̂ p X̄  ? ≤ = ≥ < > ≠  

  HA:HA: ? p σ s X n N X̄ p̂ μ  ? ≤ ≥ ≠ = < >   

b.) A Type I error in the context of this problem would be:

Select an answer Rejecting that the percentage of all students at this college who are left-handed is 11% when the percentage is really 11%. Rejecting that the percentage of all students at this college who are left-handed is 11% when the percentage is really lower than that. Rejecting that the percentage of all students at this college who are left-handed is 11% when the percentage is really higher than that. Rejecting that the percentage of all students at this college who are left-handed is lower than 11% when the percentage is really 11%. Rejecting that the percentage of all students at this college who are left-handed is higher than 11% when the percentage is really 11%. Failing to reject that the percentage of all students at this college who are left-handed is 11% when the percentage is really 11%. Failing to reject that the percentage of all students at this college who are left-handed is 11% when the percentage is really lower than that. Failing to reject that the percentage of all students at this college who are left-handed is 11% when the percentage is really higher than that. Failing to reject that the percentage of all students at this college who are left-handed is lower than 11% when the percentage is really 11%. Failing to reject that the percentage of all students at this college who are left-handed is higher than 11% when the percentage is really 11%.

c.) A Type II error in the context of this problem would be:

Select an answer Rejecting that the percentage of all students at this college who are left-handed is 11% when the percentage is really 11%. Rejecting that the percentage of all students at this college who are left-handed is 11% when the percentage is really lower than that. Rejecting that the percentage of all students at this college who are left-handed is 11% when the percentage is really higher than that. Rejecting that the percentage of all students at this college who are left-handed is lower than 11% when the percentage is really 11%. Rejecting that the percentage of all students at this college who are left-handed is higher than 11% when the percentage is really 11%. Failing to reject that the percentage of all students at this college who are left-handed is 11% when the percentage is really 11%. Failing to reject that the percentage of all students at this college who are left-handed is 11% when the percentage is really lower than that. Failing to reject that the percentage of all students at this college who are left-handed is 11% when the percentage is really higher than that. Failing to reject that the percentage of all students at this college who are left-handed is lower than 11% when the percentage is really 11%. Failing to reject that the percentage of all students at this college who are left-handed is higher than 11% when the percentage is really 11%.

Answer 1

a)
Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.11
Alternative Hypothesis, Ha: p > 0.11

b)
Type I error occurs when null hypothesis is rejected incorrectly.

Rejecting that the percentage of all students at this college who are left-handed is 11% when the percentage is really 11%.

c)
Type II error occurs when one incorrectly fails to reject the null hypothesis

Failing to reject that the percentage of all students at this college who are left-handed is 11% when the percentage is really higher than that.