The Natural Resources Canada Web site said that the national average price of regular gasoline was $1.058 per litre on July 3, 2007.It was felt that the price of gasoline in Toronto was significantly lower
Than the national average.A survey of ten different gas stations in Toronto, Ontario found the average
Price of gasoline to be $1.028 per litre with a standard deviation of $0.0263.What is the critical value
Using 0.01?
A)1.26
B)2.33
C)-1.26
D)-2.33

Question

The Natural Resources Canada Web site said that the national average price of regular gasoline was $1.058 per litre on July 3, 2007.It was felt that the price of gasoline in Toronto was significantly lower
Than the national average.A survey of ten different gas stations in Toronto, Ontario found the average
Price of gasoline to be $1.028 per litre with a standard deviation of $0.0263.What is the critical value
Using  0.01?
A)1.26 
B)2.33 
C)-1.26 
D)-2.33

Quizplus · Accepted Answer

To find the critical value with 99% confidence level and 9 degrees of freedom (n-1), we need to look at the t-distribution table. The closest value we can find to 99% confidence level with 9 degrees of freedom is 2.821. However, since the question asks for a one-tailed test (we are only interested in the lower tail as we want to determine if Toronto's price is significantly lower than the national average), we need to divide this value by 2, giving us 1.746. 
Next, we need to calculate the t-value for the sample mean using the formula:
t = (x̄ - μ) / (s / √n)
where x̄ is the sample mean, μ is the population mean (national average), s is the sample standard deviation, and n is the sample size. 
Plugging in the values, we get:
t = (1.028 - 1.058) / (0.0263 / √10) = -1.14
Since -1.14 < -1.746, we can reject the null hypothesis and conclude that the price of gasoline in Toronto is significantly lower than the national average at 99% confidence level. Therefore, we need to choose the critical value that corresponds to the rejection region in the lower tail, which is -2.33. Thus, the best choice is D. To determine if the price of gasoline in Toronto is significantly lower than the national average, we need to conduct a one-sample t-test using the formula:

t = (x̄ - μ) / (s / √n)

where x̄ is the sample mean, μ is the population mean (which is given as $1.058 per litre), s is the sample standard deviation, and n is the sample size.

Plugging in the values, we get:

t = (1.028 - 1.058) / (0.0263 / √10)
t = -3.020

To find the critical value at a significance level of 0.01 and 9 degrees of freedom (n-1), we can use a t-table or a calculator. The critical value for a two-tailed test is ±2.821.

Since our calculated t-value (-3.020) falls outside the critical region (±2.821), we can reject the null hypothesis and conclude that the price of gasoline in Toronto is significantly lower than the national average.

The best choice is D (-2.33) since it is the closest to the calculated critical value (-3.020).

The Natural Resources Canada Web Site Said That the National