Answer: [tex](15.263,\ 17.537)[/tex]
Step-by-step explanation:
According to the given information, we have
Sample size : n= 50
[tex]\overline{x}=16.40[/tex]
[tex]s=4.00[/tex]
Since population standard deviation is unknown, so we use t-test.
Critical value for 95 percent confidence interval :
[tex]t_{n-1,\alpha/2}=t_{49, 0.025}= 2.009575\approx2.010[/tex]
Confidence interval : [tex]\overline{x}\pm t_{n-1, \alpha/2}\dfrac{s}{\sqrt{n}}[/tex]
[tex]16.40\pm (2.010)\dfrac{4}{\sqrt{50}}\\\\=16.40\pm1.13702770415\\\\=16.40\pm1.1370\\\\=(16.40-1.1370,\ 16.40+1.1370)\\\\=(15.263,\ 17.537)[/tex]
Required 95% confidence interval : [tex](15.263,\ 17.537)[/tex]
The constructed 95% confidence interval for the mean time required by all adults to learn the task is; CI = (15.263, 17.537)
We are given;
Sample size; n = 50
Sample mean; x' = 16.4
standard deviation; s = 4
confidence level = 95%
Formula for confidence interval is;
CI = x' ± t(s/√n)
where t-value at 95% CI and df = 50 - 1 = 49, is t = 2.01
Thus;
CI = 16.4 ± 2.01(4/√50)
CI = 16.4 ± 1.1370
CI = (15.263, 17.537)
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