Question: The hot tamale caper. “Hot tamales” are chewy, cinnamonflavored candies. A bulk vending machine is known to dispense, on average, 15 hot tamales per bag with a standard deviation of 3 per bag. Chance (Fall 2000) published an article on a classroom project in which students were required to purchase bags of hot tamales from the machine and count the number of candies per bag. One student group claimed they purchased five bags that had the following candy counts: 25, 23, 21, 21, and 20. These data are saved in the file. There was some question as to whether the students had fabricated the data. Use a hypothesis test to gain insight into whether or not the data collected by the students were fabricated. Use a level of significance that gives the benefit of the doubt to the students

The mean number of hot tamales per bag is 15 with standard deviation 3 per kg.

It is given that the total bags are 5 with following candy counts: 25, 23, 21, 21 and 20

If the sample size is less than 30 then the hypotheses are tested using t test statistic.

The t test statistic is calculated using the following formula

Since, the mean is calculated using the following formula,

Therefore,

Also, the variance is calculated using the following formula,

Therefore,

Consider the null and the alternative hypothesis as follows,

H₀ : µ = 15

That is, the data collected by the students were fabricated.

H₀ : µ ≠ 15

That is, the data collected by the students were not fabricated.

Test statistic to test the above hypotheses is given as,

Therefore,

Now,

Level of significance, α = 0.5

Degrees of freedom, n - 1 = 4

Also, this is two tailed test.

So, from the t distribution table, the tabulated values are -2.7764 and 2.7764.

Here, t < -2.7764 and t > 2.7764.

Since, the test statistic lies in the Rejection Region, therefore the null hypothesis is rejected.So, it may conclude that the data collected by the students were not fabricated.