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A non-governmental organization (NGO) is investigating whether the average annual amount saved by households that participate in a group lending program (X population) is higher than the average annual amount saved by households that are not participating (Y population). In a random sample of 36 households that participate in a group lending program, the mean amount saved was $200, and the standard deviation of amounts saved was $40. In an independent random sample of 26 households that are not participating, the mean amount saved was $180, and the standard deviation of amounts saved was $45.
Test the null hypothesis that the population mean amount saved by households participating in a group lending program is no larger than the population mean amount saved by households that are not participating, against the alternative hypothesis that it is larger. Use a 5% level of significance. Assume that the distribution of amounts saved is approximately normal in each population (households participating in a group lending program, and households not participating), and that the distributions have a common but unknown variance.
What is the critical value and expression for the p-value?
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