A webpage's Design A is to be compared with Design B. The number of clicks on an ad is counted for 15 days for each design. The measured average and standard deviation of the daily number of clicks are given in the table below: Design A Design B Average 11 18 Standard deviation Assume the daily number of dicks is normally and independently distributed. Assume the true variances of the daily number of clicks for both designs are equal. Use a = 0.05. Conduct a hypothesis test to determine if the mean daily number of clicks for Design A, HA, Is smaller than that for Design B, HB- a. Is this a two-sided or one-sided test? Write "wo" or "one". b. How many degrees of freedom are associated with the test statistic? c. What is the pooled estimate of the common variance for both designs? Round to 2 decimal places.

A webpage's Design A is to be compared with Design B. The number of clicks on an ad is counted for 15 days for each design. The measured average and standard deviation of the daily number of clicks are given in the table below: Design A Design B Average 11 18 Standard deviation Assume the daily number of dicks is normally and independently distributed. Assume the true variances of the daily number of clicks for both designs are equal. Use a = 0.05. Conduct a hypothesis test to determine if the mean daily number of clicks for Design A, HA, Is smaller than that for Design B, HB- a. Is this a two-sided or one-sided test? Write "wo" or "one". b. How many degrees of freedom are associated with the test statistic? c. What is the pooled estimate of the common variance for both designs? Round to 2 decimal places.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!

Question

A webpage's Design A is to be compared with Design B. The number of clicks on an
ad is counted for 15 days for each design. The measured average and standard
deviation of the daily number of clicks are given in the table below:
Design A
Design B
Average
11
18
Standard deviation
Assume the daily number of dicks is normally and independently distributed. Assume
the true variances of the daily number of clicks for both designs are equal. Use a =
0.05.
Conduct a hypothesis test to determine if the mean daily number of clicks for Design
A. HA. is smaller than that for Design B, B-
a. Is this a two-sided or one-sided test?
Write "two" or "one".
b. How many degrees of freedom are associated with the test statistic?
c. What is the pooled estimate of the common variance for both designs?
Round to 2 decimal places.
d. What is the value of the test statistic?
. Round to 2 decimal
places.
e. Find the best bounds on the P-value of this test using an appropriate appendix
< P-value <
. Round to 3 decimal
table.
places.
f. Find the critical value for this test, against which the test statistic should be
compared.
Round to 3 decimal places. (Note: the sign of the
critical value should be the same as that of the test statistic.)
9. Find the confidence bound on uA - Ha to conduct this test.
Round to 2 decimal places.
h. Based on the given evidence, should you reject the null hypothesis?
Write "reject or "not reject".

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