t test, Linear Equations and linear regression
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A statistics student used a computer program to test the null hypothesis H_0: p = .5 against the one-tailed alternative, H_a: p > .5. A sample of 500 observations are input into SPSS, which returns the following results: z = .44, two-tailed p-value = .33.
a) The student concludes, based on the p-value that there is a 33% chance that the alternative hypothesis is true. DO you agree? If not, correct the interpretation.
b) How would the p-value change if the alternative hypothesis was two-tailed, H_a: p [does not equal] .5? Interpret this p-value.
In each case, graph the line that passes through the given points.
a) (1,1) and (5,5)
b) (0,3) and (3,0)
c) (-1,1) and (4,2)
d) (-6,-3) and (2,6)
Give the slow and y-intercept for each of the lines graphed above.
** Please see the attached file for the complete problem outline **
The following table (please see the attached file) is used for making the preliminary computations for finding the least squares line for the given pairs of x and y values.
a) Complete the table.
b) Find SS_xy.
c) Find SS_xx.
d) Find beta_1.
e) Find x and y.
f) Find beta_0.
g) Find the least squares line.
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Solution Summary
These solutions include a detailed explanation of the t test for proportions as well as the use of linear equations (slopes and y intercepts) in the calculation of "best fit" linear regression equation for two sets of data (dependent and independent variables). Explanations are made clear with diagrams and over 500 words of step-by-step description of the problem and its solution.
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Please see the attached file for the complete solution.
Question 1
The question specifies that the hypothesized proportion is 0.5. Under this assumption the Z statistic calculated from the Z value formula (standardization of the normal distribution using the standard error of the mean) is equal to 0.44. Now although the question says that this corresponds to two tail p value of 0.33 this is not true since the acceptance region for Z = 0.44 is 63% i.e. the probability that the proportion is equal or under 0.5 is 63% (see figure below).
(please see the attached file)
Nonetheless if this was in fact the case and the two tail p value was in fact 0.33 then since we only ...
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