Question

Please, I desperstely need help with this. These are bonus questions going towards my finals that I need so bad. And I don't mean to be a burden, but if someone does answer this to please have a decent handwriting that I can read. Thank you to whoever takes the time to help me with this, you da bomb! :)

In 4 and 5. Use the 5 step write-up we used in class. Number the steps and interpret the "formal conclusion" in setting specific terms. 4. (10 points) A politician claims that over 64% of the voters in his district agree with his stand on the gun control issue. Test his claim at the 0.04 level of significance. (Note: A random sample of 500 voters was taken from his district. 332 of them agreed with his stand. 5. (10 points) A manufacturing process is supposed to make "Widgets" that weigh 7 ounces. Test the claim that this process is making widgets that are lighter than they should be if a random sample of 15 widgets gave a mean of 6.88 ounces with a standard deviation of 0.16 ounces. Assume that the population of all widget weights is normally distributed..

Answer 1

Note : As per Chegg policy, if a post contains more than one distinct questions, we should solve one question or the question number suggested by the student.

Solving the question 4.

4)

Given                          
n = 500           Sample Size              
332 of 500 agreed with the politician's claim                          
p = 0.64           Population (Standardised) proportion (64%)              
p̂ = 332/500 = 0.664           Sample proportion of voters who agreed              
α = 0.04           Level of significance              
                          

State the null and alternative hypothesis are                                                     
Ho : p ≥ 0.64                          
H1 : p < 0.64                          
                          
This is a left tailed test                          

Compute Test Statistic
We find z, the test statistic as                           
where                           

Value of the test statistic = 1.118                          

= 1.118 z= (@n - p) p(1–p) (0.664 - 0.64) 0.64(1-0.64) 500

Find p-value
We find p-value using Excel function NORM.S.DIST                          
p-value = NORM.S.DIST(1.118, TRUE)                          
p-value = 0.8682                          

Decision :                 
0.8683 > 0.04                          
That is p-value > α                          
Hence, DO NOT Reject Ho                          
                          
Conclusion :                          
There does not exist sufficient statitical evidenceat 4% level of siginificance to show that                          
less than 64% of the voters agreed with the politician's stand                          
that is                          
the claim of the politician is true