A public health researcher wishes to study the dietary behavior of residents in Durham County. The researcher randomly contacts 35 county residents and collects data on their daily sugar intake and obtained a sample average of 37.4 grams of sugar per day and a sample standard deviation of 4.2 grams per day. Assume the mean daily sugar intake of all residents in the county is normally distributed. Construct a lower bound for a 95% confidence interval for the mean daily sugar intake of residents in Durham County using this data. (Give your answer to 3 decimal places)

Answer:

95% confidence interval for the mean daily sugar intake of residents in Durham County using this data

(35.9573, 38.8427)

Lower limit = 35.9573

Step-by-step explanation:

Step(i):-

Given that the size of the sample 'n' = 35

Given that the mean of sample x⁻ = 37.4gms

Given that the standard deviation of the sample 'S' = 4.2 gms

Level of significance = 0.05

Degrees of freedom

γ = n-1 = 35-1 = 34

t₀.₀₅ = 2.0322

Step(ii):-

95% confidence interval for the mean daily sugar intake of residents in Durham County using this data

[tex](x^{-} - t_{0.05} \frac{S}{\sqrt{n} } , x^{-} + t_{0.05} \frac{S}{\sqrt{n} } )[/tex]

[tex](37.4 - 2.0322 \frac{4.2}{\sqrt{35} } , 37.4 + 2.0322 \frac{4.2}{\sqrt{35} } )[/tex]

(37.4 - 1.4427 , 37.4+1.4427)

(35.9573, 38.8427)

Final answer:-

Lower 95% confidence interval for the mean daily sugar intake of residents in Durham County using this data

Lower limit = 35.9573

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