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One of the assumptions we sometimes need to make when performing statistical inferences is that the response variable in the population has a Normal distribution. Is it possible to check that this assumption is satisfied?

- No – we can’t really check this assumption since all data will look perfectly bell-shaped and symmetric, even if the population was not Normal.
- Yes – we can be absolutely sure the population was Normal if a plot of the data has no major outliers.
**No – we can’t really check this assumption since we don’t have the whole population, but the t distribution is robust to modest departures from Normality, so we can use it if a plot of the data has no major outliers.**- Yes – we can be absolutely sure the population was Normal if a plot of the data looks roughly bell-shaped and symmetric.
- Yes – we can be absolutely sure the population was Normal if a plot of the data looks perfectly bell-shaped and symmetric.

## Answer

No – we can’t really check this assumption since we don’t have the whole population, but the t distribution is robust to modest departures from Normality, so we can use it if a plot of the data has no major outliers.

A restaurant decides to test their oven’s thermostat to see if it is working properly, that is, if the actual temperature inside the oven is the same as the temperature to which the thermostat was set. Twenty times, the oven was set at 350 degrees and then the temperature was measured with a thermometer.

Ho: mu = 350 and Ha: mu is not equal to 350

The test statistic is equal to 3.01.

What is the p-value?

neither the Z nor the t tables are appropriate: small n, non-normal population (there is at least one extreme outlier in the sample)

either the t or the Z tables would work: large n, any shape population

Ha: mu does not equal 350

A restaurant decides to test their oven’s thermostat to see if it is working properly, that is, if the actual temperature inside the oven is the same as the temperature to which the thermostat was set. Twenty times, the oven was set at 350 degrees and then the temperature was measured with a thermometer.

Ho: mu = 350 and Ha: mu is not equal to 350

The test statistic is equal to 1.02.

What is the p-value?