Module 5. Assignment

 Question 1:

The director of manufacturing at a cookies company needs to determine whether a new machine is able to produce 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 of 49 cookies reveals a sample mean breaking strength of 69.1 pounds.

A. State the null and alternative hypothesis: 

    Null Hypothesis: The mean strength is 70.

    Alternative Hypothesis: The mean strength is not 70. 

B. Is there evidence that the machine is not meeting the manufacturer's specifications for average strength? Use a 0.05 level of significance: 

    There is no evidence that the machine does not meet the manufacturer's specification for average strength. 

We know that the critical values are +1.96 and -1.96.

We plug in what we are given to the z formula:

Z = (69.1 - 70) / (3.5 / √49)

= -0.9 / (3.5 / 7)

= -0.9 / 0.5

= -1.8

-1.8 is between 1.96 and -1.96 so it fails to reject the null hypothesis. 

C. Compute the p value and interpret its meaning 

-1.8 on the z-table is 0.03593, and it's a two-tailed test so 2 x 0.03593

p= 0.0718, which is greater than 0.05, so we don't reject the null hypothesis.

D. What would be your answer in (B) if the standard deviation were specified as 1.75 pounds?

Z = (-0.9 / (1.75 / √49)) = -3.6

-3.6, it is smaller than -1.96 so you would reject the null hypothesis.

E. What would be your answer in (B) if the sample mean were 69 pounds and the standard deviation is 3.5 pounds? 

Z = (69 - 70) / (3.5 / √49) 

= -1 / 0.5

= -2 

-2, since it is smaller than -1.96, you would reject the null hypothesis. 

Question 2:

If x̅ = 85, σ = standard deviation = 8, and n=64, set up 95% confidence interval estimate of the population mean μ.

85 ± 1.96 * (8 / √64)

= 85 ± 1.96 * 1

85 - 1.96 = 83.04 (Lower bound)

85 + 1.96 = 86.96 (Upper bound)

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The confidence interval population mean is between 84.04 and 86.96.

Question 3, using Correlation Analysis:

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