Question

A man named Sal is considering purchasing a restaurant. He asks the current owner what the distribution of the number of customers you get each day is? The owner states he has already figured that out and give Sal a distribution. Sal becomes a little suspicious and wants to see how good this distribution is. Sal then decides to observe the number of customers that come in during the week and identifies this as observe data he determines he’s going to do and hypothesis test and making the null hypothesis that the owner’s distribution is correct, and the alternative hypothesis is not right, and Sal wants a 5% significance level. Sal uses a chi-squared statistic formula. The degrees of freedom are determined as n-1. We then compare it to the chi-square distribution utilizing the df and significance value. The speaker's results were 11.44 and the chi-square critical value is 11.07 which has a greater significance meaning the speaker will reject the null hypothesis. Therefore, we will reject what the owner stated was his distribution of customers. Based on the data outcomes, should Sal have any concerns about starting the restaurant, why or why not? Can you share another example?​

Answer 1

First, we need to understand that this is a two tailed hypothesis because we are testing the null hypothesis "owner's distribution is correct" and alternate hypothesis is that "owner's distribution is not correct", this means it is a two tailed hypothesis.

The chi square statistic at 0.05 significance level is 11.07 and the observed chi square statistic is 11.44 which is more than 11.07, so the result is significant and we can reject the null hypothesis.

So, we can say that the owner's distribution is incorrect. Yes, Sal must have concerns about starting the restuarant because the owner's distribution is incorrect which means Sal needs more data to confirm that starting the restaurant is not an bad idea.

For example, we can determine whether there is any relationship between the number of cars visiting the petrol pump and amount of petrol filled.

null hypothesis;- there is no relationship between the the number of cars visiting the petrol pump and amount of petrol filled.

Alternate hypothesis:- there is a significant relationship betweeen the number of cars visiting the petrol pump and amount of petrol filled.

The chi square critical value at 0.05 is 5.90 and calculated chi square value is 6.45 which shows that the result is significant because the calculated chi square is greater than the critical chi square value

thus, we can say that we have enough evidence to support the claim that there is significant relationship between the number of cars visiting the petrol pump and amount of petrol filled.