Below are the SPSS results of a one-sample t-test. Use the SPSS results to answer Questions 3 and 4.One-Sample Statistics NMeanStd. DeviationStd. Error MeanIncrFed$, 11 prgms11395.5762.453( a ) One-Sample Test Test Value = 5tdfSig. (2-tailed)Mean Difference95% Confidence Interval of the DifferenceLowerUpperIncrFed$, 11 prgms( b )( c ).0005.576.4333.7186Replace “a,” “b,” and “c” in the tables above with the correct values. (Note that the population mean is 5.) Round to the third decimal place.At the .05 level of significance (two-tailed test), do we reject the null hypothesis?

Let xi; (i=1,2,...,n) be the random sample of size n from the normal population with mean μ and variance σ2. To test whether there is any significant difference between population mean and sample meanx¯, the procedure is: Null hypothesis: there is no significance difference between the sample mean and population mean. Alternative hypothesis: there is a significance difference between the sample mean and population mean. Test statistics: t=x¯-μoS/n Here, S is standard deviation and μo is specified population mean. Test statistics follows the Student's t-distribution with (n-1) degree of freedom. Now compute the p-value associated with the calculated t value then, compare it with level of significance, we will accept or reject the hypothesis accordingly. if p-value is greater than the given level of significance, we cannot reject the hypothesis. if p-value is less than the given level of significance, we cannot accept the hypothesis.Question-3:From the given One-sample statistics Table, we get that the following: n=1139x¯=5.576S=2.453 We know that for sample mean, the standard error is given as: S.E(x¯)=S/n Put the given values in it, we get S.E(x¯)=S/n=2.453/1139=2.453/33.74907=0.07268 Therefore, the value in place of (a.) is 0.073.It is given that n=1139 so, the degree of freedom of test statistics will be: n-1=1139-1=1138 It is given that population mean is 5 so, μo=5. The test statistics will be calculated as follows: t=x¯-μoS/n=5.576-50.07268 ...(from (a))=0.5760.07268=7.9252 Therefore, in the given One-sample Test Table, the values in place of (b.) and (c.) are 7.925 and 1138 respectively.Question-4: For the given test, the hypothesis will be: Null hypothesis: there is no significance difference between the sample mean and population mean, i.e., μo=5. Alternative hypothesis: there is a significance difference between the sample mean and population mean i.e., μo≠5 (two-tailed). From the given One-sample Test Table, the Sign.(2-tailed) implies the p-value of test statistics at 0.05 level of significance, 1138 degree of freedom and for two tailed which is equal to 0.000. Since p-value(0.000) is less than 0.05 level of significance so, we cannot accept the null hypothesis. Therefore, the null hypothesis will be rejected.

Answered: Below are the SPSS results of a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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Below are the SPSS results of a one-sample t-test. Use the SPSS results to answer Questions 3 and 4.

One-Sample Statistics
	N	Mean	Std. Deviation	Std. Error Mean
IncrFed$, 11 prgms	1139	5.576	2.453	( a )

One-Sample Test
	Test Value = 5
t	df	Sig. (2-tailed)	Mean Difference	95% Confidence Interval of the Difference
Lower	Upper
IncrFed$, 11 prgms	( b )	( c )	.000	5.576	.4333	.7186

Replace “a,” “b,” and “c” in the tables above with the correct values. (Note that the population mean is 5.) Round to the third decimal place.

At the .05 level of significance (two-tailed test), do we reject the null hypothesis?

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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