TI-83/84 PLUS LinRegTTest y=a+bx B#0_and P#0 tb=.5789830508 S=, 1117312583 r2=,5858430396 r=.7654038409
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.
As given,
The correlation coefficient (r) between the amounts of sugar and calories in a gram of cereal. is 0.7654
r = 0.7654
The sample size is n = 16
Now we want to test the significance of the correlation coefficient at a 5% level of significance.
The most appropriate test is the significance of the correlation coefficient test.
Let be the population correlation coefficient between the variables (the amounts of sugar and calories in a gram of cereal.).
To test the significance the null hypothesis is given as
That is there no is a significant correlation between the variables.
Vs the alternative hypothesis is given as
That is there is a significant correlation between the variables.
Now obtaining the test statistic.
The test statistic is given as
t = 4.45
The degree of freedom is given as
Df = n -2
= 14
Now obtaining the p-value.
Since the hypothesis is two-tailed the p-value for test statistic t = 4.45 with df = 14 is given as
P-value = 0.000549 Using the MS-EXCEL command (T.DIST.2T( 4.45,14))
Decision rule: -
At 5% level of significance
Reject the null hypothesis if p-value < 0.05
Accept otherwise.
Since p-value = 0.000549 < 0.05
We reject the null hypothesis.
Conclusion: -
At 5% level of significance, there is sufficient evidence to conclude that there is a significant correlation between the variables (the amounts of sugar and calories).
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