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A sample of 25 one-year-old girls had a mean weight of 24.1 pounds with a standard deviation of pounds. Assume that the population of weight
Question
A sample of 25 one-year-old girls had a mean weight of 24.1 pounds with a standard deviation of pounds. Assume that the population of weights is normally distributed. A pediatrician claims that the standard deviation of the weights of one-year-old girls is less than pounds. Do the data provide convincing evidence that the pediatrician’s claim is true
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Mathematics
4 years
2021-08-11T18:27:06+00:00
2021-08-11T18:27:06+00:00 1 Answers
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Answer:
Paedtricians claim isn’t true.
Step-by-step explanation:
The hypothesis :
H0 : σ = 7
H0 : σ > 7
The test statistic ; χ² :
χ² = [(n – 1) * s²] ÷ σ²
n = 25 ; s = 4.3, σ = 7
χ² = [(25 – 1) * 4.3²] ÷ 7²
χ² = [(24 * 4.3²] ÷ 49
χ² = 443.76 / 49
χ² = 9.056
At α = 0.01 ; critical value = 42.980
Since critical value > test statistic, we fail to reject the null, H0.