The economic dynamism, which is the index of productive growth in dollars for countries that are...

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 listed in the table below. Compute a 95% confidence interval for the mean 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

Table: Economic Dynamism ($) of Middle Income Countries

Step 1: State the question

Step 2: Identify the information

State the random variables and parameters in words
State the null and alternative hypotheses and level of significance
Determine the type of test this is, then state and check the assumptions for this type of test

Step 3: Perform calculations

Find the sample statistics
Find the test statistic
Find the p-value
State the conclusion (compare p and alpha and decide to reject H_o or fail to reject H_o)

Step 4. Interpret (answer the original question in a complete sentence)

Solutions

Expert Solution

we cannot define null and alternative hypotheses here because the claim about a population mean is not provided.

the question is to find out the 95% confidence interval for the mean economic dynamism of middle-income countries.

the random variables is the economic dynamism of middle-income countries.

we will use here t-test to find the confidence interval because the population standard deviation is not known.

using excel>addin>phstat>confidence interval

we have

Confidence Interval Estimate for the Mean

Data
Sample Standard Deviation	9.071147897
Sample Mean	43.87265385
Sample Size	26
Confidence Level	95%

Intermediate Calculations
Standard Error of the Mean	1.778998467
Degrees of Freedom	25
t Value	2.0595
Interval Half Width	3.6639

Confidence Interval
Interval Lower Limit	40.21
Interval Upper Limit	47.54

the 95% confidence interval for the population mean economic dynamism of middle-income countries is (40.21,47.54)

we are 95% confident that the population mean economic dynamism of middle-income countries lies in between (40.21,47.54)

orchestra answered 1 year ago

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