Vinnie is trying to modify a die by rounding off some edges.He is trying to increase the probability of rolling a 5.a) What is the probability of rolling a 5 with a fair die?p =b) Vinnie wants to see, "Do I have statistically significant evidence that my altered die will roll a 5 moreoften than a fair die?" What should he use as as the null and alternative hypothesis for this test?Но:H1:He tests his die by rolling it 4100 times, and the die comes up five 738 times during these rolls.c) Find p and the corresponding z-score for Vinnie's sample data.=Z =d) Find the p-value which corresponds to the test statistic you just found.Then sketch a bell curve that shows the expected value of p (if Ho is true), you sample statistic, p , thecorresponding z-scores and the p-value on your sketch.p-value =e) Tell me whether you "reject Ho" or "fail to reject Ho" when testing at the 5% significance level andwrite your conclusion in 'plain English'.f) Explain how you confidence interval from Assignment 22.10 could have helped predict the outcome ofthis hypothesis test.

a). A fair die has 6 faces with numbers 1, 2, 3 , 4, 5, 6 having one number on each face. let p = probability rolling a 5 with fair die = number of favourable casesexhaustive numberof cases = 16 b). Under the null hypothesis you have to state that there is no chance of getting a 5 with altered die more often than with a fair die that is chance of getting a 5 with altered die and with a fair die is equal H0 : P = 16 H1 : there is an evidence that altered die will roll a 5 more often than a fair die that is H1 : P > 16 therefore, test is a one tailed test. c). Die is rolled 4100 times i.e. n = 4100 let X = number of times a die comes up with 5 = 738 p^ = proportion of a die comes up with 5 = Xn = 7384100 = 0.18 Test statistic Z = p^-PPQn here P is the value under H0 and Q = 1-P = 1 - 16 = 56 Z = 0.18-1615×564100 = 0.013330.0063757 = 2.0908 p^ = 0.18 and Z = 2.0908d). Calculation of p value: Since the test is a one tailed test, P value is the probability of Z value greater than 2.0908 that is P value = P (Z > 2.0908) = 1 - P (Z < 2.0908) = 1 - 0.9817 = 0.0183 here P (Z < 2.0908) = 0.9817 is obtained from cumulative probability normal distribution table. therefore, P value of test statistic is 0.0183here X =number of times a 5 rolled follows Binomial distribution with n = 4100 and P mean of X =Expected value of X = nP Expected value of p = E (p) = E (Xn) = 1nE (X) = 1n(nP) = P = 16 under H0 p^ = 0.18 Z score = 2.0908 P value = 0.0183 Sketch the above values roughly on the bell shaped curve gives the following picture. you can get the exact picture on plotting these values on the graph sheet. e). level of significance 5% that is α = 0.05 here P value = 0.01863 obtained in (d) < α = 0.05 therefore, reject null hypothesis H0 that is there is an evidence that altered die will roll a 5 more often than a fair die.

Math

Statistics

Vinnie is trying to modify a die by rounding off some edges. He is trying to increase the probability of rolling a 5. a) What is the probability of rolling a 5 with a fair die? p = b) Vinnie wants to see, "Do I have statistically significant evidence that my altered die will roll a 5 more often than a fair die?" What should he use as as the null and alternative hypothesis for this test? Ho: H1: He tests his die by rolling it 4100 times, and the die comes up five 738 times during these rolls. c) Find p and the corresponding z-score for Vinnie's sample data. %3D Z = d) Find the p-value which corresponds to the test statistic you just found. Then sketch a bell curve that shows the expected value of p (if Ho is true), you sample statistic, p , the corresponding z-scores and the p-value on your sketch. p-value = e) Tell me whether you "reject Ho" or "fail to reject Ho" when testing at the 5% significance level and write your conclusion in 'plain English'.

Vinnie is trying to modify a die by rounding off some edges. He is trying to increase the probability of rolling a 5. a) What is the probability of rolling a 5 with a fair die? p = b) Vinnie wants to see, "Do I have statistically significant evidence that my altered die will roll a 5 more often than a fair die?" What should he use as as the null and alternative hypothesis for this test? Ho: H1: He tests his die by rolling it 4100 times, and the die comes up five 738 times during these rolls. c) Find p and the corresponding z-score for Vinnie's sample data. %3D Z = d) Find the p-value which corresponds to the test statistic you just found. Then sketch a bell curve that shows the expected value of p (if Ho is true), you sample statistic, p , the corresponding z-scores and the p-value on your sketch. p-value = e) Tell me whether you "reject Ho" or "fail to reject Ho" when testing at the 5% significance level and write your conclusion in 'plain English'.

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

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

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Vinnie is trying to modify a die by rounding off some edges.
He is trying to increase the probability of rolling a 5.
a) What is the probability of rolling a 5 with a fair die?
p =
b) Vinnie wants to see, "Do I have statistically significant evidence that my altered die will roll a 5 more
often than a fair die?" What should he use as as the null and alternative hypothesis for this test?
Но:
H1:
He tests his die by rolling it 4100 times, and the die comes up five 738 times during these rolls.
c) Find p and the corresponding z-score for Vinnie's sample data.
=
Z =
d) Find the p-value which corresponds to the test statistic you just found.
Then sketch a bell curve that shows the expected value of p (if Ho is true), you sample statistic, p , the
corresponding z-scores and the p-value on your sketch.
p-value =
e) Tell me whether you "reject Ho" or "fail to reject Ho" when testing at the 5% significance level and
write your conclusion in 'plain English'.
f) Explain how you confidence interval from Assignment 22.10 could have helped predict the outcome of
this hypothesis test.

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