1 hour = 3600 seconds and 1 mole = 5,280 feet. Make a conjecture about how you could convert a speed of 15 miles per hour to fee
1 answer:
We know that speed (rate) is equal to distance over time.
The current unit of distance is miles, and we want to convert it to feet. The unit of time is hours, and we want seconds. In order to do this, we need to create a conversion factor.
Since
and 
, we will use these are our conversion factors.
The goal in a dimensional analysis problem like this is for your units to work out. Remember, we want feet per second.
We write
.
You may wonder why in the conversion factor, we chose to put feet over miles and hours over seconds. This is again because we want our units to cancel. If you have one unit the numerator and the same one in the denominator, the units cancel out.
In sum, the answer is 22 ft/s.
The current unit of distance is miles, and we want to convert it to feet. The unit of time is hours, and we want seconds. In order to do this, we need to create a conversion factor.
Since
The goal in a dimensional analysis problem like this is for your units to work out. Remember, we want feet per second.
We write
You may wonder why in the conversion factor, we chose to put feet over miles and hours over seconds. This is again because we want our units to cancel. If you have one unit the numerator and the same one in the denominator, the units cancel out.
In sum, the answer is 22 ft/s.
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Answer:
If we compare the p value and the significance level for example we see that
so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can conclude that the mean annual premium in Pennsylvania is significantly lower than the national mean annual premium of 1503 at 5% of significance.
Step-by-step explanation:
1) Data given and notation
represent the mean annual premium value for the sample
represent the sample standard deviation for the sample
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean annual premium in Pennsylvania is lower than the national mean annual premium, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:
(1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
P-value
The first step is calculate the degrees of freedom, on this case:
Since is a one side left tailed test the p value would be:
Conclusion
If we compare the p value and the significance level for example we see that
so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can conclude that the mean annual premium in Pennsylvania is significantly lower than the national mean annual premium of 1503 at 5% of significance.