1. A baby's height at birth has a Normal distribution with mean unknown and standard deviation equal to 1.88cm. You obtain a sample of 40 babies, and in this sample the average height is 51.9cm. Test the hypothesis that the mean height at birth is equal to 51.4cm against the two-tailed alternative hypothesis using a 1% significance level.

2. You are designing a program that will distribute malaria nets in Mali. In order to estimate the cost of your program, you need to know how many beds are owned, on average, by households in Bamako, the capital of Mali. You find a research report published by the local government that states that each household has, on average, 2 beds. However, a research colleague mentions that she observed an average of 1.5 beds per household in a sample of 40 households.

(a) What is the sampling distribution of the sample mean number of beds per household in Bamako, Mali?

(b) You know the standard deviation of the number of beds per household in Mali is 1.8. Based on the sample your colleague observed, would you be able to conclude that the average number of beds per household is smaller than 2, using a 5% significance level? Show all the relevant steps.

3. In a sample of 51 consumers the average weekly cost of vaping was 152 dollars. Suppose you know that the standard deviation of weekly cost of vaping in the population is 115 dollars. Using a 10% significance level, would you be able to conclude that the average weekly cost of vaping in the population is larger than 130 dollars?