Use the table to answer both questions. In a packing plant, a machine packs cart
ID: 3232371 • Letter: U
Question
Use the table to answer both questions.
In a packing plant, a machine packs cartons with jars. It is hypothesized that the old machine will pack slower on average (that is, have a higher average time) than the new machine. To test that hypothesis, a researcher collected a sample from both machines and recorded the time each machine took to pack a carton.
The following table shows the sample data summary collected from the two machines.
1. Assume that the p-value is 0.04 and Type I error is 0.05. What is the correct conclusion?
a) There is no statistical evidence at the 0.05 signicant level to conclude that the new machine sample mean packaging time is higher than old machine sample mean packaging time.
b) There is no statistical evidence at the 0.05 signicant level to conclude that the new machine population mean packaging time is higher than old machine population mean packaging time.
c) There is statistical evidence at the 0.04 signicant level to conclude that the new machine population mean packaging time is higher than old machine population mean packaging time.
d) There is statistical evidence at the 0.05 signicant level to conclude that the new machine sample mean packaging time is higher than old machine sample mean packaging time.
e) There is statistical evidence at the 0.05 signicant level to conclude that the new machine population mean packaging time is higher than old machine population mean packaging time.
PLEASE EXPLAIN!
2. Assume that the p-value is 0.04(Prob > t = 0.04, Prob < t = 0.96 and Prob > |t| = 0.08). Suppose now the researcher is interested to build condence interval of the dierence between new machine population mean packaging time and old machine population mean packaging time. Which is the largest condence interval which will not contain 0?
a) 3%
b) 80%
c) 90%
d) 95%
e) 99%
Data Summary Machine Sample Std Dev Sample Size Sample Mean New 35 13.80 2257 42 Old 11.70 5.21Explanation / Answer
Answer:
1. Assume that the p-value is 0.04 and Type I error is 0.05. What is the correct conclusion?
a) There is no statistical evidence at the 0.05 signicant level to conclude that the new machine sample mean packaging time is higher than old machine sample mean packaging time.
b) There is no statistical evidence at the 0.05 signicant level to conclude that the new machine population mean packaging time is higher than old machine population mean packaging time.
c) There is statistical evidence at the 0.04 signicant level to conclude that the new machine population mean packaging time is higher than old machine population mean packaging time.
d) There is statistical evidence at the 0.05 signicant level to conclude that the new machine sample mean packaging time is higher than old machine sample mean packaging time.
Answer: e) There is statistical evidence at the 0.05 signicant level to conclude that the new machine population mean packaging time is higher than old machine population mean packaging time.
The test is significant at 0.05 level.( calculated p=0.04 < 0.05 level of significance.)
2. Assume that the p-value is 0.04(Prob > t = 0.04, Prob < t = 0.96 and Prob > |t| = 0.08). Suppose now the researcher is interested to build condence interval of the dierence between new machine population mean packaging time and old machine population mean packaging time. Which is the largest condence interval which will not contain 0?
a) 3%
b) 80%
Answer: c) 90%
d) 95%
e) 99%
The test is significant at 0.10 level of significance.( .( calculated p=0.08 < 0.10 level of significance.)
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