Surname 1. Student’s Name. Course. Date. Solution to Da

Surname 1
Student’s Name
Course
Date
Solution to Data Management
Question 1
The weights are measured using a digital weighing machine with an accuracy level of 0.05
grams. The table 1 shows the weights.
Table 1: Weight of Twenty Cookies obtained from local Supermarket
Weight (g) Weight (g)
586 538
384 497
534 486
564 550
454 530
453 427
455 461
544 389
594 385
562 456
Source: Author (2019)
The weights are measured using a digital weighing machine with an accuracy level of
0.05 grams. Let population mean be represented by μ, sample mean by X . Then, under the
assumption that the sample weights of cookies in table are normally distributed the
confidence interval for the population mean is given by the formula:
X − S
√ n tn −1 , α
2
≤ μ ≤ X + S
√ n tn−1 , α
2
Where: S – sample standard deviation, n – sample size (number of cookies whose
weights were measured), α – significance level, 5%, and tn−1 , α
2 - critical t-value. The
population standard deviation of the eight of the cookies is unknown. From excel, X =492.45
, S = 67.01, n = 20, tn−1 , α
2
=t19, 0.025=¿2.093. Therefore, the 95% confidence interval is
calculated as follows:
492.45−( 67.01
√20 ) x 2.093 ≤ μ≤ 492.45+ ( 67.01
√20 ) x 2.093