12. According to the Central Limit Theorem, the sample standard deviation (𝑠) may be used as an estimate of the population standard deviation (𝜎) when the value of 𝜎 is unknown. Which of the following is the correct test statistic to be used for Central Limit Theorem?                  *A. p-testB. z-testC. t-testD. Pearson r

Central Limit Theorem for sampling distribution is valid only when:Select one:a. Large samples drawn from any independent and identically distributed populationb. The population follows normal distributionc. Samples are drawn from any independent and identically distributed populationd. The population follows a normal distribution and the sample size should be at least 30

The central limit theorem states that:a.The mean of a population is equal to the mean of the sampleb.The sample mean will always be equal to the population meanc.The sampling distribution of the sample mean approaches a normal distribution as the sample size increasesd.The sample mean is always greater than the population mean

When conducting a hypothesis test about p we can assume the test statistic Z=P̂ −pp(1−p)n√𝑍=𝑃^−𝑝𝑝(1−𝑝)𝑛 approximately follows a standard normal distribution if:Question 5Select one:a.the data is normally distributedb.the data is continuousc.np≥5 or n(1−p)≥5𝑛𝑝≥5 or 𝑛(1−𝑝)≥5 d.np≥5 and n(1−p)≥5

The central limit theorem states that if a random sample of size n is drawn from a population, then the sampling distribution of the sample mean:Group of answer choicesis approximately normal if n ≥ 30.is approximately normal if the underlying population is normal.has the same variance as the population.is approximately normal if n < 30.

When is the z-statistic used to estimate the population mean?a.When the population standard deviation is knownb.When the population standard deviation is unknownc.When the sample size is smalld.When the sample size is large