STAT 110 - Assignment 6 (45 points) Due Sunday, October 4th

1.  In the 1980’s it was generally believed that autism affected about 5% of the nation’s children. Some people believe that the increase in the number of chemicals in the environment has led to an increase in the incidence of autism. A recent study examined 384 children and found that 46 of them showed signs of some form of autism. Is this evidence that the level of autism has increased?

a.  Define the population of interest. (1 pt)

b.  Define the sample. (1 pt)

c.  What is the parameter of interest to the researchers? (1 pt.)

d.  What is the statistic and give its value? (1 pt.)

e.  State the null and alternative hypotheses, both in words and using values of the parameter. (3 pts.)

Ho:

Ha:

f.  Is this an upper-tail or lower-tail test? Explain. (2 pts.)

g.  Give the p-value for the test. Use the binomial table to find this. (2 pts.)

h.  State the conclusion from the test. Be sure to use the p-value in your discussion. (3 pts.)

i.  Find a 95% CI for the proportion of children exhibiting signs of autism today. Be sure to report the sample proportion, the standard of error of the sample proportion, the margin of error, and the upper/lower confidence limits. (4 pts.)

j.  Interpret this interval for the researcher. (2 pts.)

2.  NC Birth Weight Study

One of the issues we looked at earlier in the course was whether or not women who smoked during pregnancy had a higher chance of having a child with a low birth weight (< 2,500 g). In a sample of 2,213 mothers who did not smoke during their pregnancy, 179 had infants with a low birth weight and in a sample of 278 mothers who smoked during pregnancy 36 gave birth to infants with low birth weights. Find a confidence interval for the proportion of infants born with low birth weights to these two populations of women.

a.  What are the two populations of interest in this study? (2 pts.)

b.  For both populations what is the parameter of interest? (1 pt.)

c.  Using the data above find the sample proportions for both populations. (2 pts.)

d.  Find confidence intervals for the proportion of infants with low birth weights in these two populations. (6 pts.)

e.  Based on these confidence intervals can we conclude that mothers who smoke during pregnancy are at a higher risk of having a low birth weight infant than women who do not smoke during pregnancy? Explain. (2 pts.)

3.  2012 STAT 110 WSU Student Survey Data

Using the 2012 STAT 110 Student Survey Data (on course website) do the
following:

a.  Find and interpret a 95% CI for the percentage of WSU students with tattoos. (4 pts.)

b.  Find and interpret a 95% CI for the percentage of WSU students who have Mac laptop. Does this interval suggest that a majority (over 50%) of students prefer Mac laptops? Explain. (4 pts.)

c.  Nationally it is estimated 30% of college students smoke cigarettes. Find a 95% confidence interval for the percent of WSU students who smoke cigarettes. Does this interval suggest that the percent of WSU students who smoke is lower than the national percentage? Explain. (4 pts.)

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