Michael drew a triangle with the sides measuring 12.5 centimeters, 30 centimeters, and 32.5 centimeters. Using the Pythagorean t
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Answer:
Test statistic (t-value) of this one-mean hypothesis test is -2.422.
Step-by-step explanation:
We are given that according to a survey, the average American person watches TV for 3 hours per week. She surveys 19 New Yorkers randomly and asks them about their amount of TV each week, on average. From the data, the sample mean time is 2.5 hours per week, and the sample standard deviation (s) is 0.9 hours.
We have to test if the amount of TV in New York City is less than the national average.
Let Null Hypothesis, :
3 {means that the amount of TV in New York City is less than the national average}
Alternate Hypothesis, :
> 3 {means that the amount of TV in New York City is more than the national average}
The test statistics that will be used here is One-sample t-test statistics;
T.S. = ~
where, = sample mean time = 2.5 hours per week
= sample standard deviation = 0.09 hours
n = sample size = 19
So, <u>test statistics</u> = ~
= -2.422
Therefore, the test statistic (t-value) of this one-mean hypothesis test (with σ unknown) is -2.422.
Answer:
(a) <em>H₀</em>: <em>μ</em> ≤ 10. vs. <em>Hₐ</em>: <em>μ</em> > 10.
(b) The test statistic value is 1.86.
(c) The critical value to test the phone manufacturer's claim is 1.301.
(d) The battery life of the new touch screen phone is not more than 10 hours.
Step-by-step explanation:
In this case we need to determine the significance of the claim made by the phone manufacturer, that the battery life of the new touch screen phone is more than twice as long as that of the leading product.
The information provided is:
(a)
The hypothesis can be defined as follows:
<em>H₀</em>: The battery life of the new touch screen phone is not more than 10 hours, i.e. <em>μ</em> ≤ 10.
<em>Hₐ</em>: The battery life of the new touch screen phone is more than 10 hours, i.e. <em>μ</em> > 10.
(b)
As the population standard deviation is not provided, we will use a <em>t</em>-test for single mean.
Compute the test statistic value as follows:
The test statistic value is 1.86.
(c)
The significance level of the test is, <em>α</em> = 0.10.
The degrees of freedom will be:
Compute the critical value as follows:
*Use a <em>t</em>-table for the value.
Thus, the critical value to test the phone manufacturer's claim is 1.301.
(d)
Decision rule:
If the test statistic value is less than the critical value then the null hypothesis will be rejected and vice-versa.
t = 1.86 > t₀.₁₀, ₄₄ = 1.30
The calculated <em>t</em>-value of the test is more than the critical value.
The null hypothesis will not be rejected.
Thus, it can be concluded that the battery life of the new touch screen phone is not more than 10 hours.
Answer:
The value of given limit problem is 0.
Step-by-step explanation:
The given limit problem is
We need to find the value of given limit problem.
Divide the numerator and denominator by the leading term of the denominator, i.e.,
Apply limit.
We know that .
Hence, the value of given limit is 0.