Which type of error can the statistician have made in the correct conclusion of this hypothesis test? (This is not an error that can be avoided.) Can we state the probability with which this error will occur? If so, state the value.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question

Multiparty problem....need help on last two problems g and h.

In the following two hypothesis test problems, the test statistic (z-
score) will be given. Following these is a separate problem for which
you will have to calculate the z-score using the appropriate formula.
1. Swimming at local beaches is affected by the number of bacteria in the
water. Bacteria numbers are monitored by taking water samples. In the
summer, the mean number of E.Coli bacteria in a water sample at local
beaches has usually been 97. The standard deviation is known to be
15. If this August 62 water samples from beaches around Annapolis
were analyzed and the mean number of E. Coli bacteria found to be
102, does this mean that summertime E. Coli bacteria levels have
increased? Use a significance level of 1% for this test. (Note: In part
(d), the test statistic (z-score) is GIVEN.)
а)
102
97
o =
15
n =
62
a =
0.01
b) Why is a hypothesis test based on the normal distribution justified?
(Explain. Don't be too brief and use appropriate terminology.)
The standard deviation is known therefore, the given hypothesis test
is based on normal distribution.
c) State the hypotheses in symbols:
: H=102
: ">102
d) z = 2.62 is the test-statistic for this hypothesis test. Use it to find
the p-value.
(Give the p-value to four decimal places) p value is 0.0044
e) Will H. be rejected? (Include the numbers for your decision) Reject
Но
) Write a conclusion in context. (This is the answer to the hypothesis
test. Make sure it includes context.)There is significant evidence to
support the claim that E. coli bacteria levels have increased.
g) Which type of error can the statistician have made in the correct
conclusion of this hypothesis test? (This is not an error that can be
avoided.)
h) Can we state the probability with which this error will occur? If so,
state the value.
Transcribed Image Text:In the following two hypothesis test problems, the test statistic (z- score) will be given. Following these is a separate problem for which you will have to calculate the z-score using the appropriate formula. 1. Swimming at local beaches is affected by the number of bacteria in the water. Bacteria numbers are monitored by taking water samples. In the summer, the mean number of E.Coli bacteria in a water sample at local beaches has usually been 97. The standard deviation is known to be 15. If this August 62 water samples from beaches around Annapolis were analyzed and the mean number of E. Coli bacteria found to be 102, does this mean that summertime E. Coli bacteria levels have increased? Use a significance level of 1% for this test. (Note: In part (d), the test statistic (z-score) is GIVEN.) а) 102 97 o = 15 n = 62 a = 0.01 b) Why is a hypothesis test based on the normal distribution justified? (Explain. Don't be too brief and use appropriate terminology.) The standard deviation is known therefore, the given hypothesis test is based on normal distribution. c) State the hypotheses in symbols: : H=102 : ">102 d) z = 2.62 is the test-statistic for this hypothesis test. Use it to find the p-value. (Give the p-value to four decimal places) p value is 0.0044 e) Will H. be rejected? (Include the numbers for your decision) Reject Но ) Write a conclusion in context. (This is the answer to the hypothesis test. Make sure it includes context.)There is significant evidence to support the claim that E. coli bacteria levels have increased. g) Which type of error can the statistician have made in the correct conclusion of this hypothesis test? (This is not an error that can be avoided.) h) Can we state the probability with which this error will occur? If so, state the value.
Expert Solution
steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Linear Equations
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman