To test a newly formulated protein bar designed to improve running performance, 10 distance runners performed two trials. All the participants ate the new protein formula bar on the first trial. In the second trial, the same participants ate the regular (old) protein bar. Thirty minutes after consuming the bar the participant ran for 2 hours on a treadmill. At the end of the two trials, performed on consecutive days for each participant, the distance each participant ran (in km) was recorded. The data is below. Runner New formula Old formula 1 10.6 10.5 2 11.2 10.9 3 10.3 10.2 4 11.9 11.6 5 9.8 9.7 6 11.1 10.8 7 12.1 11.9 8 10.9 10.8 9 9.7 9.8 10 10.3 10.3 a) Calculate a 99% confidence interval for the population mean difference in run distance after eating the newly formulated protein bar compared to the old protein bar. b) Carry out the appropriate hypothesis test using a two-sided alternative - at a 0.01 significance level. H0: ________________________________ HA: ________________________________ Name of test: __________________________ Test Statistic: Define the rejection region: Calculate the p-value: Conclusion in context of the study:
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
To test a newly formulated protein bar designed to improve running performance, 10 distance runners performed two trials. All the participants ate the new protein formula bar on the first trial. In the second trial, the same participants ate the regular (old) protein bar. Thirty minutes after consuming the bar the participant ran for 2 hours on a treadmill.
At the end of the two trials, performed on consecutive days for each participant, the distance each participant ran (in km) was recorded. The data is below.
|
Runner |
New formula |
Old formula |
|
1 |
10.6 |
10.5 |
|
2 |
11.2 |
10.9 |
|
3 |
10.3 |
10.2 |
|
4 |
11.9 |
11.6 |
|
5 |
9.8 |
9.7 |
|
6 |
11.1 |
10.8 |
|
7 |
12.1 |
11.9 |
|
8 |
10.9 |
10.8 |
|
9 |
9.7 |
9.8 |
|
10 |
10.3 |
10.3 |
a) Calculate a 99% confidence interval for the population mean difference in run distance after eating the newly formulated protein bar compared to the old protein bar.
b) Carry out the appropriate hypothesis test using a two-sided alternative - at a 0.01 significance level.
H0: ________________________________
HA: ________________________________
Name of test: __________________________
Test Statistic:
Define the rejection region:
Calculate the p-value:
Conclusion in context of the study:
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