Question 1. A port CEO wants to study the proportion of ships arriving at his port on time. How many ships must be included in the sample if the CEO wants the error to be within 0.02 and a confidence level of 95% if:
a) there is no information available that could be used as an estimate of the Population proportion?
b) a previous study suggests that 75% of ships arrive on time?
Question 2. It is believed that 70% of a university department's graduate assistantships are given to international students. A random sample of 50 graduate assistants is taken.
a) Assume that the population proportion is 0.70. Explain the sampling distribution of the sample proportion in this case.
b) Find the expected value and the standard error of the sampling distribution of the sample proportion.
c) What is the probability that the sample proportion will be between 0.65 and 0.73?
d) What is the probability that the sample proportion will be within ±0.05 of the population proportion?
Question 3. A random sample of 250 households in a large city revealed that the mean number of televisions per household was 2.76. From previous analyses, we know that the population standard deviation is 1.8. Use this information to answer the following question(s).
a) Can we conclude that at the 5% significance level the true mean number of Televisions per household are at least 2.5?
b) Calculate the p-value.
c) Compute the probability of a Type II error if the true mean number of televisions per household is 3.
Question 4. A shipping economist studies the relationship between the value per tonne of containerized cargo (x) and the freight rate charged by shipping lines for a same shipping route (y). The following table shows the values of x and y for ten shipments:
A) Find the least squares regression line showing the relationship between x as the independent variable and y as the dependent variable.
A) Find the least squares regression line showing the relationship between x as the independent variable and y as the dependent variable.
c) Calculate and comment on the value of the coefficient of determination of the Linear regression model.
d) Suggest how the results of the linear regression analysis can be improved.