Part 1

docx

School

Technical University of Mombasa *

*We aren’t endorsed by this school

Course

Subject

Statistics

Date

Nov 24, 2024

Type

docx

Pages

Uploaded by handelwriter

P-values and Significant Tests – Part 1 Name Institution Course Professor Date

P-values and Significant Tests – Part 1 The objective of this study is to compare the average data speeds of two carriers, Verizon and AT&T using data obtained from 50 airports. The analysis is performed using the statistical tool MS Excel. Descriptive statistics highlighting the mean data speeds of the two carriers is shown below: T-MOBILE 8.6 7.0 From the above output, Verizon has an average data speed of 17.6 Mbps whereas AT&T has an average of 10.7Mbps. The descriptive statistics suggest that Verizon has a higher average data speed compared to AT&T. To determine whether Verizon is significantly faster than AT&T, a two-sample t-test assuming unequal variances was conducted. Null Hypothesis: The average data speed for the carrier Verizon is less than or equal to that of AT&T H 0 : μ verizon ≤μ AT ∧ T Alternative Hypothesis: The average data speed for Verizon is greater than that of AT&T H 1 ;μ verizon > μ AT ∧ T The test is conducted at the 0.05 alpha level of significance. This means that the probability of committing a type 1 error (rejecting the null hypothesis when it is actually true) is 0.05 (Bonovas and Piovani, 2023). The test itself is right-tailed given that the alternative hypothesis focuses on the mean of Verizon being greater than that of AT&T. The rejection

region for the test thus occurs on the right tail of the distribution. Results from the test are shown below: t-Test: Two-Sample Assuming Unequal Variances VERIZON Mean 17.598 Variance 256.548 Observations 50 Hypothesized Mean Difference 0 df 73 t Stat 2.71448 P(T<=t) one-tail 0.00414 t Critical one-tail 1.66600 P(T<=t) two-tail 0.00828 From the output, the test statistic is obtained as t = 2.71448 while the one-tailed p-value is given as 0.0041. Since the p-value is less than the 0.05 level of significance, the null hypothesis is rejected. This means that at the 95% significance level, there is enough evidence to support the claim that the average data speed of Verizon is significantly greater than that of AT&T. Therefore, we can conclude that Verizon is significantly faster than AT&T since the null hypothesis was rejected. The two-sample t-test was conducted given that the two samples (Verizon and AT&T) are independent from each other (Kim, 2015) and the objective was to compare their average data speeds.

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

References Bonovas, S., & Piovani, D. (2023). On p-Values and Statistical Significance. Journal of Clinical Medicine, 12(3), 900. Kim, T. K. (2015). T test as a parametric statistic. Korean journal of anesthesiology, 68(6), 540- 546.