1-Suppose that the fuel comsumption of cars for the same model is normally distributed. A random sample
of ten new cars of the same model are randomly selected and their fuel consumption (l/100 km) is
determined by subjecting them to a road test of 500 km. Their mean fuel consumption is 7.97 (l/100 km)
and their variance fuel consumption is 8.10(l/100 km). The standard error of the sample mean is
(1) 2.521
(2) 0.285
(3) 1.111
(4) 0.810
(5) 0.90
ANSWER: 5
2-A manufacturing company packages peanuts for Piedmont Airlines. The individual packages weigh 1.4
grams with a standard deviation of 0.6 grams. For a flight of 152 passengers receiving the peanuts, the
probability that the average weight of the packages is less than 1.3 grams is
(1) 0.0202
(2) 0.2040
(3) 0.9798
(4) 0.4798
(5) 2.0500
ANSWER: 1
3-The proportion of coaches who spend more than 120 minutes at the sport is 0.023.
Out of 1000 coaches, the expected number who will spend more than 120 minutes at the sport is:
(1) 1023
(2) 120000
(3) 23
(4) 977
(5) 63.24
ANSWER:3
4-Consider an infinite population with a mean of 160 and a standard deviation of 25. A random sample of
size 64 is taken from this population.
The standard deviation of the sample mean equals:
(1) 12.649
(2) 25.000
(3) 2.560
(4) 3.125
(5) 0.391
ANSWER: 4
5-The following five statements refer to using the t-table in the correct way for a given probability. However,
one statement is incorrect. Find the incorrect statement.
(1) For 25 degrees of freedom, the value of A that corresponds to P (t ¡Ý A) = 0.025 is A = 2.060
(2) For 25 degrees of freedom, the value of A that corresponds to P (t ¡Ü A) = 0.10 is A = −1.316
(3) For 25 degrees of freedom, the value of A that corresponds to P (−A ¡Ü t ¡Ü A) = 0.99 is A = 2.787
(4) For 85 degrees of freedom, the value of A that corresponds to P (t ¡Ü A) = 0.025 is A = 1.988
(5) For 85 degrees of freedom, the value of A that corresponds to P (−A ¡Ü t ¡Ü A) = 0.98 is A = 2.371
ANSWER: 4
6-A random sample of 30 women drank an average of 15 cups of coffee per week during examination finals,
with the sample standard deviation equal to 3 cups. A upper limit of an approximate confidence interval
with 95% of the population average cup drunk is
(1) 15.000
(2) 13.9265
(3) 16.1201
(4) 1.60735
(5) 16.0735
ANSWER: 3
7-A statistics practitioner wishes to test the following hypothesis: H0 : ¦Ì = 600 against H1 : ¦Ì < 600
A sample of 50 observations yielded the statistics: mean x = 585 and standard deviation sx = 45. The
test statistic of a test to determine whether there is enough evidence at the 10% significance level to reject
the null hypothesis is
(1) 2.3570
(2) 0.3333
(3) 16.6667
(4) 23.570
(5) −2.3570
ANSWER: 2
To answer each of these questions, we need to apply statistical concepts and formulas. I will explain how to find the answer for each question.
1. To find the standard error of the sample mean, we divide the standard deviation of the population by the square root of the sample size. In this case, the standard deviation is the square root of the variance. So, the answer is the square root of 8.10 divided by the square root of 10, which is approximately 0.90. Therefore, the answer is 5.
2. To find the probability that the average weight of the packages is less than 1.3 grams, we need to calculate the z-score. The z-score formula is (sample mean - population mean) divided by (standard deviation divided by the square root of the sample size). Since we have the sample mean, population mean, standard deviation, and sample size, we can use these values to calculate the z-score. Then, we can look up the corresponding probability in the z-table or use a statistical calculator. The answer is 0.0202, which corresponds to option 1.
3. The expected number of coaches who will spend more than 120 minutes at the sport can be calculated by multiplying the proportion by the total number of coaches. In this case, the expected number is 0.023 multiplied by 1000, which equals 23. Therefore, the answer is option 3.
4. The standard deviation of the sample mean can be calculated by dividing the population standard deviation by the square root of the sample size. In this case, the population standard deviation is given as 25, and the sample size is 64. So, the answer is 25 divided by the square root of 64, which is 25 divided by 8, equaling 3.125. Therefore, the answer is option 4.
5. The incorrect statement can be identified by comparing the given values with the correct values obtained from the t-table or using a statistical tool. Option 4 states that for 85 degrees of freedom, the value of A corresponding to P(t ≤ A) = 0.025 is A = 1.988. However, the correct value should be A = 1.960. Therefore, option 4 is the incorrect statement.
6. To calculate the upper limit of an approximate confidence interval, we need to use the formula: sample mean + (critical value * standard deviation divided by the square root of the sample size). The critical value can be obtained from a t-table or a statistical tool based on the desired confidence level and degrees of freedom. In this case, since the confidence interval is 95%, the critical value can be determined using a t-table with 29 degrees of freedom. After calculating the critical value, we can substitute the given values into the formula and find the upper limit. The answer is approximately 16.1201, corresponding to option 3.
7. To find the test statistic for a hypothesis test, we need to calculate the z-score using the formula: (sample mean - hypothesized mean) divided by (standard deviation divided by the square root of the sample size). After calculating the z-score, we can compare it to the critical value for the given significance level (10%). If the test statistic is less than the critical value, we can reject the null hypothesis. In this case, the answer is approximately 0.3333, corresponding to option 2.
Please note that while the explanations provided above should generally lead to the correct answers, there may be some slight variations due to rounding or other nuances in statistical calculations.