Question

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).

Answer 1

Question

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 table provided below ("SOCR data 2008," 2013). 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.

            

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

What is the appropriate test for this case?   

What is the null hypothesis?   

What is the alternative hypothesis?   

Determine if this test is left-tailed, right-tailed, or two-tailed.

What is the significance level?

What is the test statistic?

What is the p-value?

Do we reject the null hypothesis?

What is the conclusion?  

What is 95% confidence interval for the population mean?

Interpret the confidence interval.

Answer

Claim: Mean economic dynamism of middle-income countries is less than 60.29

The sample size = 26

Since the population standard deviation is not known

We use the one sample mean T test for this scenario

Null Hypothesis: Mean economic dynamism = 60.29

Ho: M = 60.29

Alternate hypothesis: Mean economic dynamism < 60.29

Ha: M < 60.29

It is a left tailed test because the alternate hypothesis contains the “less than < “ symbol

Given: significance level = 5% or 0.05

.

For test statistic the formula:

T = (x bar – M) / ( s / sqrt( n))

.

Where x bar = sample mean = 43.87

M = population mean = 60.29

S = sample standard deviation = 9.07

N = sample size = 26

.

On plugging these values we get:

T = (43.87 – 60.29) / (9.07 /sqrt(26))

T = -9.23

.

Df = n -1

Df = 26-1 = 25

P value for T = -9.23 , df = 25 and left tailed test is 0.000

Since the P value 0.000 < alpha 0.05 , we reject the null

Thus we conclude that the mean value is than 60.29 , and conclude that there is sufficient evidence t support the claim that mean economic dynamism of middle-income countries is less than the mean of high-income countries.

.

For confidence interval the formula is:

X bar – t* s/sqrt( n) , x bar + t * s/ sqrt(n)

.

T critical for 95% confidence level df = 25 can be obtained from the T table

We get: T = 2.060

On plugging all the values we get:

43.87 -2.060 * 9.07/sqrt(26) , 43.87 +2.060 *9.07 /sqrt(26)

40.2057, 47.5343

.

Interpretation: There is 95% of the chance that the mean value will lie in the range of (40.2057, 47.5343). Since the value 60.29 does not fall in this interval and the upper limit of the interval is less than 60.29 we conclude that the mean of the middle income countries is less than 60.29