the average height of students at uh from an srs of 14 students gave a standard deviation of 2.5 feet. construct a 95% confidence interval for the standard deviation of the height of students at uh. assume normality for the data. a) (2.812, 10.028) b) (1.812, 4.028) c) (1.312, 8.028) d) (0.812, 6.028) e) (3.812, 8.028) f) none of the above

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08-11-2022
Mathematics

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the average height of students at uh from an srs of 14 students gave a standard deviation of 2.5 feet. construct a 95% confidence interval for the standard deviation of the height of students at uh. assume normality for the data. a) (2.812, 10.028) b) (1.812, 4.028) c) (1.312, 8.028) d) (0.812, 6.028) e) (3.812, 8.028) f) none of the above

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MahimZuberi MahimZuberi · Answer 1 · 2022-11-15T21:17:13-05:00

The following is the 95% confidence interval for the standard deviation of UH students' height: CI = (1.81, 4.028) that is option B is correct.

What is standard deviation?

The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation indicates that the data are grouped around the mean, whereas a high standard deviation shows that the data are more dispersed. The standard deviation gauges how widely the data deviates from the mean. When comparing data sets that may have the same mean but a different range, it is helpful.

Here,

The formula for the standard deviation's confidence interval is given as CI = √[(n - 1)s²/(χ²ₙ ₋ ₁, α/2)], √[(n - 1)s²/(χ²ₙ ₋ ₁, (1 - α)/2)]

Number of participants; n = 14 D F = n - 1 = 14 - 1 = 13

Deviation from the mean; s = 2.5

Significant level; = 1 - 0.95 = 0.05

Confidence level; CL = 95% = 0.95

As a result, using an online Chi-square distribution table, we have:

χ²₁₃, ₀.₀₂₅ = 24.736

(χ²₁₃, ₀.₉₇₅) = 5.01

CI = √[(13 * 2.5²/(24.736)], √[(13 * 2.5²/(5.01)]

CI = (1.81, 4.03) (1.81, 4.03)

The range with a 95% confidence level for the height standard deviation of UH students is as follows: CI = (1.81, 4.028), so option B is the proper one.

To know more about standard deviation,

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