Question

Question 3 options:

The economic dynamism, which is the index of productive growth (in dollars), for countries that are designated by the World Bank as middle-income are in following table ("SOCR data 2008," 2013).

Table: Economic Dynamism of Middle Income Countries

25.8057	37.4511	51.915	43.6952	47.8506	43.7178	58.0767
41.1648	38.0793	37.7251	39.6553	42.0265	48.6159	43.8555
49.1361	61.9281	41.9543	44.9346	46.0521	48.3652	43.6252
50.9866	59.1724	39.6282	33.6074	21.6643

Countries that are considered high-income have a mean economic dynamism of 60.29. Do the data show that the mean economic dynamism of middle-income countries is less than the mean for high-income countries? Test at the 5% level.

(i) Which of the following statements correctly defines the null hypothesis H_O?

A.  μ < $60.29  

B.  p < $60.29

C.  μ = $60.29

D.  p = $60.29

(ii) Which of the following statements correctly defines the alternative hypothesis H_A?

A.  μ < $60.29  

B.  p < $60.29

C.  μ = $60.29

D.  p = $60.29

(iii) Enter the level of significance α used for this test:

Enter in decimal form. Examples of correctly entered answers:  0.01    0.02    0.05    0.10

(iv)  Determine sample mean x

Enter answer to nearest ten-thousandth, without "$" sign. Examples of correctly entered answers:

11.2385      0.0079     3.0500      7.4000

(v)  Determine sample standard deviation s :

Enter in decimal form to nearest thousandth. Do not enter "$" sign. Examples of correctly entered answers:

    0.002    9.050    11.300    210.715

(vi)  Determine degrees of freedom df

Enter answer as integer number without sign

(vii) Calculate and enter test statistic

Enter value in decimal form rounded to nearest ten-thousandth, with appropriate sign (no spaces). Examples of correctly entered answers:

–2.0140      –0.0307        +0.6000        +1.0009

(viii) Using tables, calculator, or spreadsheet: Determine and enter p-value corresponding to test statistic.

Enter value in decimal form rounded to nearest thousandth. Examples of correctly entered answers:

0.000     0.001     0.030     0.600      0.814 1.000

(ix) Comparing p-value and α value, which is the correct decision to make for this hypothesis test?

A. Reject H_o

B. Fail to reject H_o

C. Accept H_o

D. Accept H_A

(x) Select the statement that most correctly interprets the result of this test:

A. The result is statistically significant at .05 level of significance. Evidence supports the claim that the mean economic dynamism for a middle-income country is less than 60.29, the mean for high-income countries.

B. The result is statistically significant at .05 level of significance. There is not enough evidence to support the claim that the mean economic dynamism for a middle-income country is less than 60.29, the mean for high-income countries.

C. The result is not statistically significant at .05 level of significance. Evidence supports the claim that the mean economic dynamism for a middle-income country is less than 60.29, the mean for high-income countries.

D. The result is not statistically significant at .05 level of significance.   There is not enough evidence to support the claim that the mean economic dynamism for a middle-income country is less than 60.29, the mean for high-income countries.

Enter letter corresponding to most correct answer

Answer 1

(i) The Null Hypothesis: Option C: H0: = 60.29

(ii) The Alternative Hypothesis: Option A: H0: < 60.29

(iii) The Level of significance used = 0.05

(iv) The sample mean x = 43.8727

(v) The sample standard deviation, s = 9.071

(vi) The degrees of freedom = n - 1 = 26 - 1 = 25

(vii) The Test statistic = (x - ) / [s / sqrt(n)] = (43.8727 - 60.29) / [9.071 / sqrt(26)] = -9.2285

(viii) The p value (left tail) = 0.000

(ix) Since p value is < , Option A: Reject H0.

(x) Option A: The result is statistically significant at 0.05 level of significance. There is enough evidence to support the claim that the mean economic dynamism for a middle income country is less that 60.29, the mean for high income countries

_____________________________________________________________

Calculation for the mean and standard deviation:

Mean = Sum of observation / Total Observations

Standard deviation = SQRT(Variance)

Variance = Sum Of Squares (SS) / n - 1, where

SS = SUM(X - Mean)².

#	X	Mean	(x - mean)2
1	25.8057	43.8727	326.42
2	41.1648	43.8727	7.33
3	49.1361	43.8727	27.70
4	50.9866	43.8727	50.61
5	37.4511	43.8727	41.24
6	38.0793	43.8727	33.56
7	61.9281	43.8727	326.00
8	59.1724	43.8727	234.08
9	51.915	43.8727	64.68
10	37.7251	43.8727	37.79
11	41.9543	43.8727	3.680
12	39.6282	43.8727	18.016
13	43.6952	43.8727	0.032
14	39.6553	43.8727	17.786
15	44.9346	43.8727	1.128
16	33.6074	43.8727	105.376
17	47.8506	43.8727	15.824
18	42.0265	43.8727	3.408
19	46.0521	43.8727	4.750
20	21.6643	43.8727	493.213
21	43.7178	43.8727	0.024
22	48.6159	43.8727	22.498
23	48.3652	43.8727	20.183
24	58.0767	43.8727	201.754
25	43.8555	43.8727	0.000
26	43.6252	43.8727	0.061

n	26
Sum	1140.689
Average	43.8727
SS	2057.143104
Variance = SS/n-1	82.28572418
Std Dev	9.071