A survey by the Arthur Andersen Enterprise Group/ National Small Business United attempted to determine what the leading challenges are for the growth and survival of small businesses. Although the economy and finding qualified workers were the leading challenges, several others were listed in the results of the study, including regulations, listed by 30% of the companies, and the tax burden, listed by 35%. Suppose that 71% of the companies listing regulations as a challenge listed the tax burden as a challenge. Assume these percentages hold for all small businesses. If a small business is randomly selected, determine the following probabilities:

a. The small business lists both the tax burden and regulations as a challenge.

b. The small business lists either the tax burden or regulations as a challenge.

c. The small business lists either the tax burden or regulations but not both as a challenge.

d. The small business lists regulations as a challenge given that it lists the tax burden as a challenge.

e. The small business does not list regulations as a challenge given that it lists the tax burden as a challenge.

f. The small business does not list regulations as a challenge given that it does not list the tax burden as a challenge.

Government Waste In a Gallup poll 513 national adults aged 18 years or older who consider themselves to be Republican were asked, “Of every tax dollar that goes to the federal government in Washington, D.C., how many cents of each dollar would you say are wasted?” The mean wasted was found to be 54 cents with a standard deviation of 2.9 cents. The same question was asked of 513 national adults aged 18 years or older who consider themselves to be Democrat. The mean wasted was found to be 41 cents with a standard deviation of 2.6 cents. Construct a 95% confidence interval for the mean difference in government waste, . Interpret the interval.