Question

In: Statistics and Probability

Data 1 and Data 2 represent two samples from your production on Monday and Tuesday of...

Data 1 and Data 2 represent two samples from your production on Monday and Tuesday of this week. Calculate the P-value when comparing the population averages of these two groups.

Please include Excel calculations.

Data 1

Strength
252 280 287 272 261 260 279 279 273
266 280 284 280 267 269 260 268 260
259 255 288 296 263 289 282 283 268
281 274 267 280 282 277 276 269 279
287 283 266 262 267 290 275 274 305
269 267 268 282 270 261 270 264 298

Data 2

Strength
255 262 268 271 279 282 287
256 263 268 272 279 282 289
259 264 268 273 279 283 261
260 266 269 274 279 283 217
260 266 269 274 280 283 247
261 267 269 275 280 284 238
261 267 270 276 280 287 220
261 267 270 277 281 287 235

Solutions

Expert Solution

To compare population averages of two groups.

In this problem the sample size is greater than 30. Hence we use Z test to compare two population averages.

Hypothesis,

Ho : There is no significant difference between two population means i.e. 1 = 2

H1 : There is significant difference between two population means i.e. 12

Data set 1 Data set 2
252 255
266 256
259 259
281 260
287 260
269 261
280 261
280 261
255 262
274 263
283 264
267 266
287 266
284 267
288 267
267 267
266 268
268 268
272 268
280 269
296 269
280 269
262 270
282 270
261 271
267 272
263 273
282 274
267 274
270 275
260 276
269 277
289 279
277 279
290 279
261 279
279 280
260 280
282 280
276 281
275 282
270 282
279 283
268 283
283 283
269 284
274 287
264 287
273 287
260 289
268 261
279 217
305 247
298 238
220
235

Variance is calculated by using var function in excel.

Variance of data set 1 = 125.964

Variance of data set 1 = 225.1221

We run this Z test in excel by using data analysis toolpack.

Go to data analysis toolpack and select Z test for means.

Input range of two data sets and variance calculated above and our alternative hypothesis is two sided so substitute mean difference is zero. The output of test as follows,

z-Test: Two Sample for Means
Variable 1 Variable 2
Mean 274.1296296 268.5714286
Known Variance 125.964 225.1221
Observations 54 56
Hypothesized Mean Difference 0
z 2.205235305
P(Z<=z) one-tail 0.013718793
z Critical one-tail 1.644853627
P(Z<=z) two-tail 0.027437587
z Critical two-tail 1.959963985

From above table,

Test statistic Z = 2.2052

and the p-value is 0.0274

Here level of significance is = 0.05

p-value <

Hence reject H0

Conclusion : There is significant difference between two population averages i.e. 12

orchestra answered 1 year ago
Next > < Previous

Related Solutions

1. On Monday, you consume 15 eggs and 25 wines. On Tuesday, the price of eggs...
1. On Monday, you consume 15 eggs and 25 wines. On Tuesday, the price of eggs goes up and the price of wine goes down. The Monday and Tuesday budget lines cross at (20,20). Use indifference curves to justify your answers to the following questions: a) Might you choose to consume 24 eggs on Tuesday? b) Can you determine on which day you are happier? For parts c) and d), assume that you choose to consume exactly 18 eggs on...
Exercise 3 The data in the table represent the "Exam Scores" for two random samples of...
Exercise 3 The data in the table represent the "Exam Scores" for two random samples of students. The first group of = 6 students were under active-learning course, and the second group of = 6 students were under traditional lecturing. Note that the standard deviations in the Active group is = 3.43 and in the Traditional group is = 3.03. Active learning Traditional learning 0 7 5 0 7 8 8 2 0 4 3 3 Please answer the following...
Exercise 3 The data in the table represent the "Exam Scores" for two random samples of...
Exercise 3 The data in the table represent the "Exam Scores" for two random samples of students. The first group of n1 = 6 students were under active-learning course, and the second group of n2 = 6 students were under traditional lecturing. Note that the standard deviations in the Active group is s1= 3.43 and in the Traditional group is s2 = 3.03. Active learning Traditional learning 0 7 5 0 7 8 8 2 0 4 3 3 Please...
The data of the samples taken from two piles are as follows. Yığın-1 Yığın-2 Sample Volume...
The data of the samples taken from two piles are as follows. Yığın-1 Yığın-2 Sample Volume 12 9 Sample Average 34,56 41,73 Sample Variance 4,02 3,21 5% significance level, a) Is there evidence that the 2nd stack variance is less than 3.1? b) Is there evidence that the two stack variances are not equal? c) Is there evidence that the average of the first stack is smaller than the average of the second stack? What is the p-value?
The following data represent petal lengths (in cm) for independent random samples of two species of...
The following data represent petal lengths (in cm) for independent random samples of two species of Iris. Petal length (in cm) of Iris virginica: x1; n1 = 35 5.1 5.9 6.4 6.1 5.1 5.5 5.3 5.5 6.9 5.0 4.9 6.0 4.8 6.1 5.6 5.1 5.6 4.8 5.4 5.1 5.1 5.9 5.2 5.7 5.4 4.5 6.4 5.3 5.5 6.7 5.7 4.9 4.8 5.7 5.2 Petal length (in cm) of Iris setosa: x2; n2 = 38 1.6 1.9 1.4 1.5 1.5 1.6...
The following data represent petal lengths (in cm) for independent random samples of two species of...
The following data represent petal lengths (in cm) for independent random samples of two species of Iris. Petal length (in cm) of Iris virginica: x1; n1 = 35 5.1 5.9 6.1 6.1 5.1 5.5 5.3 5.5 6.9 5.0 4.9 6.0 4.8 6.1 5.6 5.1 5.6 4.8 5.4 5.1 5.1 5.9 5.2 5.7 5.4 4.5 6.4 5.3 5.5 6.7 5.7 4.9 4.8 5.9 5.1 Petal length (in cm) of Iris setosa: x2; n2 = 38 1.5 1.9 1.4 1.5 1.5 1.6...
The following data represent petal lengths (in cm) for independent random samples of two species of...
The following data represent petal lengths (in cm) for independent random samples of two species of Iris. Petal length (in cm) of Iris virginica: x1; n1 = 35 5.1 5.6 6.3 6.1 5.1 5.5 5.3 5.5 6.9 5.0 4.9 6.0 4.8 6.1 5.6 5.1 5.6 4.8 5.4 5.1 5.1 5.9 5.2 5.7 5.4 4.5 6.4 5.3 5.5 6.7 5.7 4.9 4.8 5.9 5.2 Petal length (in cm) of Iris setosa: x2; n2 = 38 1.5 1.9 1.4 1.5 1.5 1.6...
The following data represent petal lengths (in cm) for independent random samples of two species of...
The following data represent petal lengths (in cm) for independent random samples of two species of Iris. Petal length (in cm) of Iris virginica: x1; n1 = 35 5.3 5.7 6.5 6.1 5.1 5.5 5.3 5.5 6.9 5.0 4.9 6.0 4.8 6.1 5.6 5.1 5.6 4.8 5.4 5.1 5.1 5.9 5.2 5.7 5.4 4.5 6.4 5.3 5.5 6.7 5.7 4.9 4.8 5.8 5.2 Petal length (in cm) of Iris setosa: x2; n2 = 38 1.5 1.7 1.4 1.5 1.5 1.6...
The following data represent petal lengths (in cm) for independent random samples of two species of...
The following data represent petal lengths (in cm) for independent random samples of two species of Iris. Petal length (in cm) of Iris virginica: x1; n1 = 35 5.1 5.6 6.2 6.1 5.1 5.5 5.3 5.5 6.9 5.0 4.9 6.0 4.8 6.1 5.6 5.1 5.6 4.8 5.4 5.1 5.1 5.9 5.2 5.7 5.4 4.5 6.4 5.3 5.5 6.7 5.7 4.9 4.8 5.7 5.1 Petal length (in cm) of Iris setosa: x2; n2 = 38 1.6 1.9 1.4 1.5 1.5 1.6...
The following data represent petal lengths (in cm) for independent random samples of two species of...
The following data represent petal lengths (in cm) for independent random samples of two species of Iris. Petal length (in cm) of Iris virginica: x1; n1 = 35 5.1 5.8 6.5 6.1 5.1 5.5 5.3 5.5 6.9 5.0 4.9 6.0 4.8 6.1 5.6 5.1 5.6 4.8 5.4 5.1 5.1 5.9 5.2 5.7 5.4 4.5 6.4 5.3 5.5 6.7 5.7 4.9 4.8 5.9 5.1 Petal length (in cm) of Iris setosa: x2; n2 = 38 1.6 1.8 1.4 1.5 1.5 1.6...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT