(25 points) The local government of countryis committed to curb the consumption of tobacco among youngsters owing to its severe health effects. Previous attempts to regulate tobacco consumption have failed to produce any fruitful results. The only possible way out is to tax the consumption of tobacco. Optimal taxation would require a proper knowledge of how price sensitive the consumers are to tobacco consumption. Data is collected by selecting a small sample of individuals at random. It is known that the price elasticity of tobacco consumption follows a normal distribution. Similar studies carried out earlier report that the price elasticity of tobacco consumption has a mean 0.32. The current survey aims to verify whether the value of the mean population price elasticity is actually 0.32 or not. The given table summarizes the findings from the survey:

Number of individuals surveyed (). 23

The standard deviation of the sample (S_y) 0.34

The sample mean of price elasticity (^-) 0.47

1. (a) Specify the null and alternative hypotheses in the situation.
2. (b) Can you reject the null hypothesis at the 5% level? Explain it.
3. (c)Construct a 95% confidence interval for the mean population price elasticity.