Homework 4 (22 points)
STAT 301
Name(s) _____SOLUTION__________
Due: Thursday, February 14 th @ 11:59pm
1.
The Gerber Company sponsored a large survey of the eating habits of American infants and toddlers. Among the many questions parents were asked was whether their child had eaten fried potatoes on the day before the interview. Among the 316 toddlers 19 to 24 months old who were surveyed, 82 had eaten fried potatoes the day before the interview.
Research Question – Is there evidence that more than one third of toddlers 19 to 24
months old eat fried potatoes on a given day? a.
Identify the population of interest. (1 point) All toddlers 19 to 24 months old b.
Identify the sample. (1 point) 316 toddlers 19 to 24 months old c.
Identify the single categorical variable of interest. (1 point) Eat Potatoes? d.
Identify the parameter of interest. (1 point) p = true proportion of toddlers 19 to 24 months old that eat potatoes on a given day e.
Identify the statistic. (1 point)
ˆ
82
= 0.26
316 f.
Describe in context how the Binomial Distribution can be used to model this scenario.
(4 points)
1. n = 316 toddlers 19 to 24 months old
2. 2 outcomes – eat fried potatoes, don’t eat fried potatoes
3. P(eat fried potatoes) = 0.33 for each toddler
4. 19 to 24 month old toddlers are independent of one another g.
Determine the appropriate null and alternative hypotheses that would be used to test the research question of interest. (3 points)
H
0
: p ≤ 0.33
H a
: p > 0.33 h.
Using the BinomialProbabilities.jmp file on the course website, calculate the p-value for this study. (2 points) p-value = 0.9973
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i.
Using the p-value from part h, what conclusion can be made regarding the research question? (3 points)
There is not statistically significant evidence (since 0.9973 > 0.05) that more than one third of toddlers 19 to 24 months old eat fried potatoes on a given day.
2.
A Pew Research Center survey was given to 1931 randomly selected adult internet users and found that 1120 of them said the internet has helped them in some way with obtaining health information. a.
Using JMP, construct a 90% confidence interval for the true proportion of adult internet users who said the internet has helped them in some way with obtaining health information. Give the bounds of the interval below. (2 point)
___0.56__ ≤ p ≤ ___0.60___ b.
Interpret the 90% confidence interval found in part a. (3 points)
99% confident the true proportion of adult internet users who say the internet has helped them in some way with obtaining health information is between
0.56 and 0.60
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