1. A student in a statistics class needs to do a project and decides to find out
ID: 3150058 • Letter: 1
Question
1. A student in a statistics class needs to do a project and decides to find out if the average high school GPA of students in a statistics course at her university is higher than the average high school GPA for their university. The university’s average high school GPA of enrolled students in their year was 4.41.
She emails a survey to all of her friends that are taking statistics and asks them what their high school GPA is. Her sample contains 18 responses. She chooses a 5% level of significance. From her data, she calculates a t-test statistic of approximately 1.41 with a p-value of about 0.08. What can she conclude?
A: Nothing. The conditions for use of a t-test are not met. She cannot trust that the p-value is accurate for this reason.
B: The data is not statistically significant. In other words, the data do not provide enough evidence to conclude that the mean GPA of students taking statistics at her university is higher than 4.41.
C: The data is statistically significant. In other words, the data do provide enough evidence to conclude that the mean GPA of students taking statistics at her university is higher than 4.41.
2. In 2013, the average Girl Scout in New York City sold 96 boxes of cookies. The leader of Troop 5078 in New York City wants to know if the scouts in her troop sold more cookies than the average in New York City. She randomly samples 50 girls in Troop 5078 and records the number of boxes of cookies sold for each girl in the sample.
The troop leader finds that her Girl Scouts each sold an average of 101.1 boxes of cookies with a standard deviation of 29.3. She analyzed her data using a t-test and obtained a p-value of 0.11.
What conclusion can she draw from her data?
A: Even though 101.1 is larger than 96, it is not significantly larger than 96. In other words, the data do not provide enough evidence to conclude that the mean number of boxes of cookies sold by Girl Scouts in Troop 5078 was higher than 96.
B: Nothing. The conditions for use of a t-test were not met. She cannot trust that the p-value is accurate for this reason.
C: The sample value of 101.1 is significantly larger than 96. In other words, the data provide enough evidence to conclude that the mean number of boxes of cookies sold by Girl Scouts in Troop 5078 was higher than 96.
3. Water safety standards in southern California suggest that if a concentration of adenoviruses in the water is more than 1,000 per liter, further testing would have to be done to determine if the water was hazardous. A random sample of 45 water sources around San Diego showed an average of 1,023 adenoviruses per liter, with a standard deviation of 138.9.
Which hypothesis test should be used to determine if the water samples contain more than the allowed 1,000 adenoviruses per liter?
A: z-test for the population mean
B: t-test for the population mean
C: z-test for the population proportion
D: t-test for the population proportion
Explanation / Answer
#1 Since she did not use random sample, the correct option is:
A: Nothing. The conditions for use of a t-test are not met. She cannot trust that the p-value is accurate for this reason.
--------------------------------------------------------------------------------------------------------------------------
#2 Since p-value = 0.11 is greater than 0.05, the difference is not significant. The correct option is:
A: Even though 101.1 is larger than 96, it is not significantly larger than 96. In other words, the data do not provide enough evidence to conclude that the mean number of boxes of cookies sold by Girl Scouts in Troop 5078 was higher than 96.
--------------------------------------------------------------------------------------------------------------------------
#3 Since there is only one sample that we want to compare with population mean and also sample size is is greater than 30, we should use z-test for the population mean. The correct option is:
A: z-test for the population mean
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.