Add 0.0025 kg, 1750 mg, 2.25 g, and 825,000 μg, and express the answer in grams.
1 answer:
Answer:
6.75g
Step-by-step explanation:
The initial step is to convert all values to grams using rules of three, followed by summation.
In a rule of three calculation, the first step is identifying the measures and how they interrelate; whether their connection is direct or inverse.
In direct relationships, as one measure increases, so does the other.
In inverse relationships, as one measure increases, the other decreases.
Problems involving unit conversion, like this, illustrate a direct relationship between measures.
First step: convert 0.0025kg to grams
One kilogram equals 1000 grams, so:
1kg - 1000g
0.0025kg - xg
x = 1000*0.0025 = 2.5g
Thus, 0.0025kg is equal to 2.5g
Second step: handle 1750 mg
One gram consists of 1000mg, so:
1g - 1000mg
xg - 1750mg
1000x = 1750
x = 1.75g
Therefore, 1750 mg converts to 1.75g
2.25g is fine
Third step: convert 825,000 μg to grams
One gram consists of 1,000,000 micrograms, so:
1g - 1,000,000 μg
xg - 825,000 μg
1,000,000x = 825,000
x = 0.25g
So, 825,000 μg equals 0.25g
Final step: sum all values
0.25g + 2.25g + 1.75g + 2.50g = 6.75g
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Answer:
a) Null hypothesis:
Alternative hypothesis:
b)
Given that the p-value is lower than the significance threshold in this situation, we have sufficient grounds to reject the null hypothesis.
c)
In this case, since the p-value exceeds the significance threshold, we have adequate evidence to FAIL to reject the null hypothesis.
d)
Here again, with the p-value being less than the significance level, we can reject the null hypothesis.
Step-by-step explanation:
1) Provided data and references
represents the average of the samples
denotes the standard deviation of the samples
indicates the number of samples
is the value we are examining
defines the significance level for the test.
t represents the specific statistic of interest
indicates the p-value relevant to the test (the variable of concern)
Define the null and alternative hypotheses.
To assess if the true mean is at least 10 hours, we must set up a hypothesis:
Part a
Null hypothesis:
Alternative hypothesis:
If we consider the sample size being less than 30 and the population deviation unknown, it’s more appropriate to use a t-test to compare the actual mean with the reference value, calculated as:
(1)
Part b
In this scenario t=-2.3,
Initially, we need to calculate the degrees of freedom
Since this is a left-tailed test, the p-value is determined by:
In this instance, with the p-value being less than the significance level, we have sufficient evidence to reject the null hypothesis.
Part c
For this situation t=-1.8,
We need to find the degrees of freedom
For the left-tailed test, the p-value is given by:
In this case, since the p-value is above the significance level, we have enough grounds to FAIL to reject the null hypothesis.
Part d
For this case t=-3.6,
Firstly, we find the degrees of freedom
Since we are conducting a left-tailed test, the p-value is calculated as:
Here, with the p-value being lower than the significance threshold, we can reject the null hypothesis.