Note: You may use the Excel calculator for these exercises and submit the sheet

Question

Note: You may use the Excel calculator for these exercises and submit the sheet to ow your calculations. ercise 1 Ten individuals went on a low-fat diet for 12 weeks to lower their cholesterol. Evaluate the data below. Do you think that their cholesterol levels were significantly lowered? (Show all your work i.e. Ho and Ha, p-value, condusion in words) Ending cholesterol level 140 230 120 220 190 150 200 300 300 Difference Starting cholesterol level 140 220 110 240 180 190 360 280 Table 1 Exercise 2 Average entry level salaries for college graduates with mechanical engineering degrees and electrical engineeig degrees are believed to be approximately the same. (Source: http:/lwww.graduatingengineer.com3).A recruiting office thinks that the average mechanical engineering salary is actually lower than the average electrical engineering salary. The recruiting office randomly surveys 50 entry level mechanical engineers and 60 entry level electrical engineers. Their average salaries were $46,100 and $46,700, respectively. Their standard deviations were $3450 and $4210, respectively. Conduct a hypothesis test to determine if you agree that the average entry level mechanical engineering salary is lower than the average entry level electrical engineering salary. (Show all your work i.e. Ho and Ha, p-value, condusion in words)

Explanation / Answer

H0 : Mud = 0        Vs           H1 : Mud < 0

Where Mud is population mean difference between starting cholesterol level and ending cholesterol level.

Assume alpha = level of significance = 0.05

This is the problem of paired t-test.

We can do this test in excel.

Steps :

ENTER data into excel sheet --> Data --> Data analysis --> t-test : Paired two sample for means --> ok --> Variable 1 range : select starting data --> Variable 2 range : select ending data --> Hypothesized mean difference : 0 --> Labels --> Alpha : 0.05 --> Output range : select one empty cell --> ok

Test statistic = 1.17

P-value = 0.2706

P-value > alpha

Accept H0 at 5% level of significance.

Conclusion : There is not sufficient evidence to say that their cholesterol levels were significantly lowered.

2) Here we have to test the hypothesis that,

H0 : mu1 = mu2 Vs H1 : mu1 < mu2

where mu1 is population average entry level mechanical engineering salary

mu2  is population average entry level electrical engineering salary

Assume alpha = level of significance = 0.05

Given that,

Here we use two sample t-test assuming equal variances.

We can do two sample t test in ti-83 calculatior.

steps :

STAT --> TESTS --> 4:2-SampTTest --> ENTER --> High light on STATS --> Input all the values --> select alternative <mu2 --> ENTER --> Pooled : yes --> Calculate --> ENTER

Test statistic = -0.81

P-value = 0.2108

P-value > alpha

Accept H0 at 5% level of significance.

COnclusion : Thereis not sufficient evidence to say that one population mean is lower than other.

t-Test: Paired Two Sample for Means starting ending Mean 218 209 Variance 5173.333333 3854.444 Observations 10 10 Pearson Correlation 0.945031587 Hypothesized Mean Difference 0 df 9 t Stat 1.173913043 P(T<=t) one-tail 0.135278719 t Critical one-tail 1.833112923 P(T<=t) two-tail 0.270557437 t Critical two-tail 2.262157158

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