The margin of error corresponding to the 95% confidence interval for a sample mean constructed from a sample of size 53 is 7.94.
Margin of error is defined as the degree of the sampling errors in statistics. It can be calculated using the formula below.
MOE = z x (SD / √n)
where MOE = margin of error
z = found by using a z-score table
SD = sample standard deviation = 29.5
n = sample size = 53
At 95% confidence level, the area in each tail of the standard normal curve is 2.5, and the cumulative area up to the second tail is 97.5.
(100 - 95) / 2 = 2.5
100 - 2.5 = 97.5
Find 0.975 in the z-table to get the value of z.
At p = 0.975, z = 1.96
Plug in the values to the formula and solve for the margin of error.
MOE = z x (SD / √n)
MOE = 1.96 x (29.5/√53)
MOE = 7.94
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