Bilqees, a prospective university student who just matriculated, must decide which profession she will study towards. She has a passion for economics but will only follow her passion if she can determine whether economics graduates are paid well in the labour market (if not, she will choose to study accounting). She decides that if economics graduates earn, on average, R250 000 per year within five years of graduation she will pursue the study of economics. Bilqees asks her older sibling, an econometrician, to help her estimate the average salary of economics graduates based on a small sample using confidence interval estimation. She interviews a sample of eight recent economics graduates who are currently employed in order to investigate whether the average salary is at least as high as her requirement. These data are handed to her sibling for confidence interval estimation and are given below (measured in thousands of rands) :

X

287

196

276

252

275

325

204

185

You are Bilqees's older sibling. Assuming that the annual salary (X)is normally distributed, find a 95% confidence interval for , the true average annual salary for economics graduates by answering the questions below.

1. what is the relevant t-statistic is?

2. The estimated 95% confidence interval is Pr( fill in the blank). (fill in the blank ).

3. Choose the correct answer: If we were to re-estimate the confidence interval for the mean annual salary of economics graduates using significance level =0.1, then...

• A. the confidence limits will remain unchanged because it is still based on the same data and sample size.
• B. the interval between the lower and upper limits will decrease because, for the same sample size, a larger -value is associated with a lower t-value.
• C. this is not possible, in order to estimate confidence intervals with a different -value, we need to draw a new sample.
• D. we would need a different sample.
• E. the interval between the lower and upper limits will increase since the significance level is larger.