Final answer:
Yes, a normal distribution can be used to model the test statistic in large samples when the null hypothesis is true. This is based on the Central Limit Theorem, and is valid as long as the data is from a simple random sample or the sample size is sufficiently large if the population distribution is not normal.
Step-by-step explanation:
When the sample size is large, a normal distribution can indeed be used to model the values of the test statistic if the null hypothesis is true, so the answer to the student's question is 1) Yes. This is due to the Central Limit Theorem, which indicates that, as the sample size increases, the sampling distribution of the mean will tend to be normally distributed regardless of the shape of the population distribution, provided the sample is sufficiently large (usually, greater than 30 is considered adequate).
However, certain conditions must be met for this approximation to be appropriate: the data must come from a simple, random sample, and if the population distribution is known and not normal, then the sample size must be large. If the population standard deviation is known, a normal (z-test) distribution is used. If the population standard deviation is unknown and the sample size is large, then a Student's t-test may be used if testing a single population mean. When sample sizes are small, the data must be approximately normally distributed for the normal model to be used.