If f(x) = 3x + 2, what is f(5)?
2 answers:
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Step-by-step explanation:
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Answer:
a) Null hypothesis:
Alternative hypothesis :
b)
The rejection regin would be (-infinity;-2.82)
c)
d) 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 reject the null hypothesis, so we can conclude that the mean breaking strength of the new bonding adhesive is significantly less than 5.7Mpa at 1% of significance.
e) See below the explanation.
Step-by-step explanation:
Data given and notation
represent the mean breaking strength value for the sample
represent the sample standard deviation
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)
a) State the null and alternative hypotheses.
Is a one tailed left test.
What are H0 and Ha for this study?
Null hypothesis:
Alternative hypothesis :
b) Find the rejection region for the test using significance level=.01
First we need to find the degrees of freedom on this case:
In order to find the critical value we need to find a value on the normal standard distribution such that:
where 0.01 represent the significance level selected.
And this value is
The rejection regin would be (-infinity;-2.82)
c) Compute the test statistic
The statistic for this case 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:
d) Give the appropriate conclusion for the test
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 reject the null hypothesis, so we can conclude that the mean breaking strength of the new bonding adhesive is significantly less than 5.7Mpa at 1% of significance.
e) What conditions are required for the test results to be valid?
The first assumption made regarding t-tests concerns the scale of measurement. The assumption for a t-test is that the scale of measurement applied to the data collected follows a continuous or ordinal scale (Assumed)
The second assumption made is that of a simple random sample, that the data is collected from a representative, randomly selected portion of the total population. (Assumed)
The third assumption is the data comes from a normal distribution, bell-shaped distribution curve. (Assumed)
The fourth assumption is a reasonably large sample size is used. (For this case we can asume that a sample size of 10 is enough to conduct a t test)