A food snack manufacturer samples 15 bags of pretzels off the assembly line and weighed their contents. If the sample mean is 10.2 and the sample standard deviation is 0.25, find the 95% confidence interval of the true mean________.A. (10.06, 10.34)B. (10.07, 10.33)D. (10.14, 10.26)
Accepted Solution
A:
Answer: the correct option is AStep-by-step explanation:We want to find 95% confidence interval for the mean of the weight of pretzels. Number of samples. n = 15 bagsMean, u = 10.2Standard deviation, s = 0.25We will use the t- testDegree of freedom = n - 1 = 15 - 1= 14Alpha, a = (1-confidence interval )/2 a = (1-0.95)/2 = 0.025Looking at the t-distribution table, the corresponding z value is 2.131Confidence interval = z × standard deviation/√nConfidence interval = 2.131 × 0.25/√15Confidence interval = 0.13755545851Approximately 0.138At 95% confidence interval, The lower end is 10.2 - 0.138 = 10.062 Approximately 10.06The upper end is 10.2 - 0.138 = 10.338. Approximately 10.34