(1 point) The following data represents the calorie-content per Cream -cup servi

Question

(1 point) The following data represents the calorie-content per Cream -cup serving for 16 randomly selected flavours of Jen and Berry's Ultra-Creamy lce 270 150 170 140 160 160 290 190 190 160 170 150 110 180 170 185 It it assumed that the calorie-content per L-cup serving of Jen and Berry's Ultra-Creamy lce Cream is a normally distributed random variable (a) Construct a 95% confidence interval which estimates the mean calorie-content for a 0.5-cup of Jen and Berry's Ultra-Creamy Ice Cream (Input answers to 1 decimal place) (b) Can you conclude that the mean calorie-content per 0.5-cup is 175 V? Yes No lote: You can earn partial credit on this oroblemm

Explanation / Answer

HEre sample mean x = 177.8125 calories

Sample standard deviation s = 38.8066

sample size n = 16

standard error of the sample mean se0= s/ sqrt(n) = 38.8066/ sqrt(16) = 9.7017

(a) 95% confidence interval = x +- ta,n-1 (se0)

= 177.8125 +- 2.13145 * 9.7017 [ here dF = 15 and a = 0.05 so t0.05,15 = 2.13145 ]

= (157.134, 198.491)

or in 1 decimal place ( 157.1, 198.5)

(b) Yes, we can conclude that mean calorie content per 0.5 cup is 175 calorie so because the confidence interval does contain value of 175 calorie.

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