Question

**Q1 - Part a**

You work for the Evostuck sticky bun company. Your rivals are the Superglug

sticky bun company. You want to know whether there are more Evostuck or Superglug consumers in your city. You take a sample and find that there are more Evostick consumers in your sample. You want to see whether this is true for the whole population of the city. What statistical test would you use?

**Q1 - Part b**

You want to know if there are a significantly higher proportion of Evostuck consumers in your city than in Sacramento. What statistical test would you use?

**Q1 - Part c**

If you wanted to know if there were significantly less female consumers of Superglug in Sacramento than in San Francisco, what statistical test would you use?

**Q1 - Part d**

You had a reduced sugar version of Evostuck. You tested consumers to see if they could tell the difference, using difference tests. What statistical test would you use to check whether or not your sample of consumers noticed a difference between the two formulations?

**Q2 - Part a**

Is it easier to reject H0 at the 5% or the 1% level of significance? Give reasons:

**Q2 - Part b**

If the sample size is larger, is there a greater or lesser chance of rejecting H0? Give reasons:

**Q2 - Part c**

If a small sample rejected H0 at the 1% level of significance, would you need a smaller or larger sample to reject H0 at the 0.1% level? State your reasons:

**Q2 - Part d**

When N is large, what distribution does the binomial distribution approximate to?

**Q3**

Which of the following is **true?**

*(Hint: *Try to sketch the distributions and think about the definition of mean in comparison to median)

-In a left skewed distribution, less than 50% of the data are below the mean

-In a symmetric distribution, more than 50% of the data are below and less than 50% are above the mean

-In a left skewed distribution, roughly 50% of the data are below and 50% are above the mean

-In a right skewed distribution, less than 50% of the data are below the mean

**Q4**

The midrange is defined as the average of the maximum and the minimum.

** True or false:** This statistic is robust to outliers

Give reason to your answer!

**Q5**

You're given this dataset: 6, 2, 8, 7, 5 and asked to convert it into standard scores. Without doing any calculation (*well, you can if you want*), what is the mean and standard deviation of the standard scores? What are their units?

**Q6**

The standard deviation of a sampling distribution is often called as the standard error. Which of the following statements about sampling distribution and standard error is **false?**

**-**Standard error measures the variability in means of samples of the same size taken from different populations

-Standard error computed based on a sample standard deviation will always be lower than the standard deviation of that sample

-As the sample size increases, standard error decreases

-Sampling distributions get closer to normality as the sample size increases

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