A study conducted across the US with n = 545 children found that on average kids

Question

A study conducted across the US with n = 545 children found that on average kids are getting glasses at 5.5 years old with a standard deviation of .75 years. State a 95% confience interval for the mean age of children getting corrective lenses: I am % confident that the age of children getting glasses is between and. Another study in Europe found that children there weren't getting glasses as early. They conducted a large study of a decade long from 2000 to 2015 and found that the average age was 6.2 years. Is there statistical evidence that children in the US are getting glasses sooner at the .05 level? Set up the hypothesis: H_0: mu = H_a: mu Compute: t = and p = and state your conclusion: There (is/is not) statistically significant evidence at the level that children in the US are. Dr. P is trying to determine increase flexibility of patients struggling with arthritis in their hips. He is using water therapy to see if flexibility in patients improves over time, specifically with hamstring flexibility. Set up the null and alternative hypothesis for this t test. H_0: mu 0 AND H_a: mu 0

Explanation / Answer

1.

n = 545
mean = 5.5
Stdev = .75

95% CI for the mean age of children getting corrective lenses:

I am 95% confident that the mean age of children getting glasses is between

5.5 - 1.96*.75/sqrt(545) = 5.44 to 5.5 + 1.96*.75/sqrt(545) = 5.56

2.

Mean = 6.2 years

alpha = .05

Ho: Mu = 6.2
Ha: Mu <6.2

t = (5.5-6.2)/(.75) = -.93

The P-Value is .176298

There is not statistically significant evidence at the 95% level that children in the US are getting glasses sooner than 6.2 years

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