Question

Suppose the weights of tight ends in a football league are normally distributed such that σ 2 =1,369 . A sample of 49 tight ends was randomly selected, and the weights are given below. Use Excel to calculate the 95% confidence interval for the mean weight of all tight ends in this league. Round your answers to two decimal places and use ascending order.

Weight
300
294
155
270
218
242
150
364
298
167
297
299
221
266
261
301
269
267
219
165
198
359
240
263
160
171
169
259
196
197
268
271
200
295
258
199
260
303
264
241
220
265
262
343
321
302
364
296
170

Answer (__), (__)

Answer 1

Solution :

Given

Variance σ^2 = 1369

standard deviation σ = sqrt(1369) = 37

Level of significance = 0.05

Sample size = 49

95% Critical Z value is 1.96

Mean = 251.78 ( from data)

Using Excel

Margin of error = CONFIDENCE(alpha,standard_dev,size)

Margin of error = CONFIDENCE(0.05,37,49)

= 10.35981

ME ~ 10.36

(or)

Margin of error ME = Z * σ/sqrt(n)

= 1.96 * (37/sqrt(49))

= 1.96 * (37/7)

   ME = 10.36

95 % confidence interval is (Xbar - ME , Xbar + ME)

= (251.78 - 10.36 , 251.78 + 10.36)

95 % confidence interval = (241.42, 262.14)