A study a local high school tried to determine the mean height of females in the US. A study surveyed a random sample of 125 females and found a mean height of 64.5 inches with a standard deviation of 5 inches. Determine a 95\% confidence interval for the mean.

UkusakazaL

UkusakazaL

Answered question

2021-08-02

A study a local high school tried to determine the mean height of females in the US. A study surveyed a random sample of 125 females and found a mean height of 64.5 inches with a standard deviation of 5 inches. Determine a 95% confidence interval for the mean.
Confidence Intervalz80%1.28285%1.44090%1.64595%1.96099%2.57699.5%2.80799.9%3.291

Answer & Explanation

ruigE

ruigE

Beginner2021-08-10Added 1 answers

Step 1
Solution:
Given information:
n=125 Sample size
x=64.5 inches Sample mean
s=5 inches sample standard deviation
α=0.05 Level of significance
Step 2
The 95% confidence interval for the mean is
x±tα2,n1×sn
n is large we used zα2 instead of tα2,n1
At α=0.05
zα2=z0.05=1.96 From Z table
(64.5±1.96×5125)
(64.5±1.96×511.180339)
(64.5±1.96×0.4472135)
(64.5±0.8765384)
(64.50.8765384,64.5+0.8765384)
(63.62346,65.376538)
(63.62,65.38)
The 95% confidence interval for the mean is ( 63.62, 65.38)

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