It is generally believed that nearsightedness affects about 15% of children. A school district gives vision tests to 111 incoming kindergarten children. Use the empirical rule (68%-95%-99.7% Rule) to determine what proportion of nearsighted children we might expect to see in samples of 111 children (I'm not looking for the number of children). Assume conditions are met!
Based on your results, would you be surprised to find a sample where 20% of children were nearsighted? Find the z-score and resulting probability to make this determination, rather than just analyzing the number of standard deviations.
| for normal distribution z score =(p̂-p)/σp | |
| here population proportion= p= | 0.150 |
| sample size =n= | 111 |
| std error of proportion=σp=√(p*(1-p)/n)= | 0.0339 |
hence probability of having 20% or more children nearsighted :
| probability = | P(X>0.2) | = | P(Z>1.48)= | 1-P(Z<1.48)= | 1-0.9306= | 0.0694 |
as this probability is not less then 0.05 level of unusual events ; therefore this is not an unusual event
It is generally believed that nearsightedness affects about 15% of children. A school district gives vision tests...
It is generally believed that nearsightedness affects about 15% of children. A school district gives vision tests to 111 incoming kindergarten children. In our sample of 111 students, we find 13% of the students were nearsighted. Construct a 90% confidence interval for the number of nearsighted kindergarteners we would expect to see based on our sample. Does this support or refute the estimate of 15%? Assume conditions are met (so don't check them)! Explain in details
It is generally believed that nearsightedness affects about 13% of children in a certain region. A school district tests the vision of 178 incoming kindergarten children. How many would be expected to be nearsighted? What is the standard deviation for the number of nearsighted children in this group?
It is generally believed that nearsightedness affects about 12% of all children. A school district has registered 170 incoming kindergarten children. If a random sample of 50 kindergarten children is selected, what is the probability the sample differs from the mean by more than 1%? Round your answers to four decimal places. ( please show step by step) thanks.
Complete all parts of the question and detailed answer. 4. It is generally believed that nearsightedness affects about 12% of all children. A school district randomly selected 170 children in kindergarten and found that 10% were nearsighted. a) Categorical or Quantitative Variable? b) Is 12% a Sample statistic or Population parameter? c) Is 10% a Sample statistic or Population parameter? d) Should we use a z-distribution or t-distribution? e) Calculate a hypothesis test to test if there is a decrease...
It is believed that nearsightedness affects about 8% of all children. In a random sample of 200 children, 25 are nearsighted. Do these data provide evidence that the 8% value is inaccurate? At α = 0.05, test the claim. Find the p-value. P-value = 0.0190 P-value = 2.35 P-value = 0.05 P-value = 0.125