Past data indicate that the amount of money contributed by the working residents of large two cities to a volunteer rescue squad is normally distributed. Based on 9 observations, city 1 has a sample standard deciation of $1.10 and based on 6 observation from city 2, sample standard deviation is equal to $2.90. State and conclude your hypothesis at the 0.05 level of significance if the variance in city 1 is less than the variance in city 2.

Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude tha the variance in city 1 is less than the variance in city 2

Step-by-step explanation:

Data given

represent the sampe size for group 1

represent the sample size for group 2

represent the sample deviation for group 1

represent the sample deviation for group 2

represent the significance level provided

Confidence =0.95 or 95%

Solution to the problem  

System of hypothesis

We want to test  if the variance in city 1 is less than the variance in city 2., so the system of hypothesis are:

H0:

H1:

Calculate the statistic

The statistic is given by:

Replacing we got:

We need to find the degrees of freedom. For the numerator we have and for the denominator we have and the F statistic present 8 degrees of freedom for the numerator and 5 for the denominator.

P value

Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude tha the variance in city 1 is less than the variance in city 2

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step-by-step explanation: