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Hypothesis Testing and Correlation Analysis

The director of manufacturing at a cookies needs to determine whether a new machine is production a particular type of cookies according to the manufacturer's specifications, which indicate that cookies should have a mean of 70 and standard deviation of 3.5 pounds. A sample pf 49 of cookies reveals a sample mean breaking strength of 69.1 pounds.

A. State the null and alternative hypothesis 
 Ho = u>=  70  and alt hypo. Ho = u<70

B. Is there evidence that the machine is nor meeting the manufacturer's specifications for average strength? Use a 0.05 level of significance . 
since the data is random sample size the data seem almost approximate normal. 

C. Compute the p value and interpret its meaning? 
(xbar - mu) / (stdsqrt(n)) = (69.1 - 70)/(3.5/sqrt(49)) = -1.80 this indicted it does not fall under the region and it is rejected. 

D. What would be your answer in (B) if the standard deviation were specified as 1.75 pounds? 
based of the z table score, its out of the significant level range it will mostly likely that the machine is not meeting the manufactures specifications. 
E. What would be your answer in (B) if the sample mean were 69 pounds and the standard deviation is 3.5 pounds?
don't understand the question
d
Second Question:
If x̅ = 85, σ = standard deviation = 8, and n=64, set up 95% confidence interval estimate of the population mean μ.
 Z= 1-(0.05/2) = 1.96
Sample mean= x-bar = 85
Z*s/sqrt(n) = (1.96*8)/sqrt(64) = 1.96
CI= 85 – 1.96= 83.04
CI= 85- 1.96= 86.96
(83.04, 86.96)

The accompanying data are: x= girls and y =boys. (goals, time spend on assignment)  
a. Calculate the correlation coefficient for this data set 

[1] 0.9991175
b. Pearson correlation coefficient 

[1] 0.995622
c. Create plot of the correlation

r studio keep giving me an error when i try to plot the cor. 

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