Ch 4.5 Name: 1. It is believed that nearsightedness affects about 8% of all children. In a random sample of 194 children, 21 are nearsighted. a) To determine if our point estimate follows a nearly normal distribution, it has to pass this test: np 2 10 AND n(1-p) 210 Use this to see if our Sampling Distribution for p is approximately normal. b) Construct the hypotheses Ho and HA that are appropriate for the following question: do these data provide evidence that the 8% value is inaccurate? Make a sketch of "If Ho is true." c) What proportion of the children in this sample are nearsighted? Formula: = n d) Calculate the standard error of the sample proportion, rounding off at the fourth decimal place. Formula: SE= Po(1-Po) where po is the Null Value (from Ho and HA) n e) Calculate the test statistic using the formula: z = P - Po SE Use this result to locate where your sample proportion p is on your sketch. Draw a line there and shade the area AWAY FROM the Center. If it's a "one-tailed test" then only one side is shaded, if it's a "two-tailed test" then you will shade both sides. f) The shaded-area in your sketch is your P-value. Calculate this P-value. g) What is the conclusion of the hypothesis test? Use a significance level of 0.05 h) Follow-up with a 95% confidence interval for the population proportion. State your answer "in context." Does it agree with your Hypothesis Test? Explain