You wish to test the following at a significance level of α=0.10α=0.10. H0:p=0.53H0:p=0.53 H1:p<0.53H1:p<0.53You obtain a sample of size n=140n=140 in which there are 71 successful observations.For this test, we use the normal distribution as an approximation for the binomial distribution.For this sample...The test statistic (zz) for the data = (Please show your answer to three decimal places.)The p-value for the sample = (Please show your answer to four decimal places.)The p-value is...less than (or equal to) ααgreater than ααBase on this, we should...reject the null hypothesisaccept the null hypothesisfail to reject the null hypothesisAs such, the final conclusion is that...The sample data suggest that the population proportion is not significantly less than 0.53 at the significant level of αα = 0.10The sample data suggest that the population proportion is significantly less than 0.53 at the significant level of αα = 0.10.

Name: You wish to test the following at a significance level of α=0.10α=0.10
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Description: You wish to test the following at a significance level of α=0.10α=0.10. H0:p=0.53H0:p=0.53 H1:p<0.53H1:p<0.53You obtain a sample of size n=140n=140 in which there are 71 successful observations.For this test, we use the normal distribution

Answered: You wish to test the following at a…

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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You wish to test the following at a significance level of α=0.10α=0.10.

H0:p=0.53H0:p=0.53
H1:p<0.53H1:p<0.53

You obtain a sample of size n=140n=140 in which there are 71 successful observations.

For this test, we use the normal distribution as an approximation for the binomial distribution.

For this sample...

The test statistic (zz) for the data = (Please show your answer to three decimal places.)
The p-value for the sample = (Please show your answer to four decimal places.)
The p-value is...
- less than (or equal to) αα
- greater than αα
Base on this, we should...
- reject the null hypothesis
- accept the null hypothesis
- fail to reject the null hypothesis
As such, the final conclusion is that...
- The sample data suggest that the population proportion is not significantly less than 0.53 at the significant level of αα = 0.10
- The sample data suggest that the population proportion is significantly less than 0.53 at the significant level of αα = 0.10.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Expert Solution

Step 1

From the given information,

The null hypothesis is,

H0: p=0.53

The alternative hypothesis is,

H1:p<0.53(left-tailed)

The level of significance is,α=0.10.

The sample size is , n=140

The number of successful observations is, x =71

The sample proportion is,

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