The European Social Survey (ESS) is an academically driven cross-national survey that has been conducted across Europe established in 2001. The data from the ESS survey showed that 43 %% of Spanish families have their children living with them. A researcher surveyed a random sample of n = 142 Spanish in his town, 71 of them said that their children were living with them.

Research Question: "Is the proportion of people living with their children in the researcher's town equal to the proportion of Spanish citizens living with their children?"

Answer the following questions by choosing the most correct option or typing the answer.

(1 mark) Let X represents the number of people who live with their children, what is the sampling distribution for X?

• Right-skewed distribution
• Binomial distribution
• Uniform distribution
• Left-skewed distribution
• Normal distribution

(2 marks) The most appropriate test for these data is:

• one sample t-test for a population mean
• one sample t-test for a population proportion
• one sample z-test for a population proportion
• one sample z-test for a population mean

For the remaining questions you may assume that any relevant assumptions for the chosen statistical test have been met.

(1 mark) The null hypothesis is that the population proportion is Answer (Hint: this is the value of p0p0 in the H0H0: p=p0p=p0)

(2 marks) The absolute value of the test statistic is equal to Answer (3dp)

(2 marks) Is the p-value for this test statistic greater or less than 0.05? Answer

• the p-value is greater than 0.05
• the p-value is less than 0.05

(2 marks) The test shows the proportion of people living with their children in the researcher's town was Answer

• Significantly different from the population (could be greater)
• Significantly different from the population (could be lower)
• Not significantly different from the population.