Question

D.        Suppose a nationwide study reports that the average price for a gallon of self-serve regular unleaded gasoline is $3.76. You believe that the figure is higher in your area of the country. You decide to test this claim for your part of the United States by randomly calling gasoline stations. Your random survey of 25 stations produces the following prices as shown in the table. Assume gasoline prices for a region are normally distributed. Do the data you obtained provide enough evidence to reject the null hypothesis? Use a 1% level of significance. Interpret your result.

$3.87	$3.89	$3.76	$3.80	$3.97
3.80	3.83	3.79	3.80	3.84
3.76	3.67	3.87	3.69	3.95
3.75	3.83	3.74	3.65	3.95
3.81	3.74	3.74	3.67	3.70

D1.      The appropriate test should be:

            a.         a right-hand-side tailed t-test for the mean unleaded gasoline price in your area.

            b.         a right-hand-side tailed Z-test for the proportion of gasoline price in your area that                        is higher than the national average.

            c.         a left-hand-side tailed t-test for the mean unleaded gasoline price in your area.

            d.         a Chi-square test for the mean unleaded gasoline price in your area.

D2.      The appropriate observed value or test statistic is

            a.         1.9578

            b.         2.575

            c.         2.101

            d.         1.645

D3.      The appropriate critical value is, under a 1% level of significance:

            a.         2.575

            b.         1.645

            c.         2.492

            d.         2.101

D4.      Is it true that the true average unleaded gasoline price in your area is higher than the         national average of $3.76, based on the results of your test?

            a.         Yes

            b.         No, sample evidence does not support this statement.

            c.         Can’t decide.

Answer 1

1. As the test has less than 30 observations and the observations follows normal distribution with population variance is unknown, we will use t -test in that case.

As our alternative hypothesis is average price per gallon is higher than national average and we want to accept this. Therefore we need to use right tailed t -test to effectively reject null hypothesis with 99% confidence level.

Hence option A is correct. B&D are wrong as they use incorrect test statistic. And C is using the incorrect direction for our hypothesis.

2. Data for our hypothesis is calculated below.

Observations	Sample	Deviation from mean	Squared deviation
1	3.87	0.08	0.01
2	3.89	0.10	0.01
3	3.76	-0.03	0.00
4	3.80	0.01	0.00
5	3.97	0.18	0.03
6	3.80	0.01	0.00
7	3.83	0.04	0.00
8	3.79	-0.00	0.00
9	3.80	0.01	0.00
10	3.84	0.05	0.00
11	3.76	-0.03	0.00
12	3.67	-0.12	0.02
13	3.87	0.08	0.01
14	3.69	-0.10	0.01
15	3.95	0.16	0.02
16	3.75	-0.04	0.00
17	3.83	0.04	0.00
18	3.74	-0.05	0.00
19	3.65	-0.14	0.02
20	3.95	0.16	0.02
21	3.81	0.02	0.00
22	3.74	-0.05	0.00
23	3.74	-0.05	0.00
24	3.67	-0.12	0.02
25	3.70	-0.09	0.01
Mean	3.79	Sum of squared deviation (A)	0.19
	0.09	B(Variance)=A/(25-1)	0.01
		C(Std Deviation) = B^0.5	0.09

T statistic value = 3.79 - 3.76/ (0.09/25^0.5) => 1.9578 (A) is correct.

3. Appropriate critical value would be 24 degrees of freedom, at 1% = >2.492 (C) is correct.

4. As our t statistic value (1.95) is falling under critical value (2.49). we cannot reject null hypothesis. Therefore Option B is correct!!.

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