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.
1
2
| 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 agoRelated Solutions
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