Average entry level salaries for college graduates with mechanical engineering degrees and electrical engineering degrees are believed to be approximately the same. 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, conclusion in words)
'Usa today reported on the results of an opinion poll in which 63% of adults said they would sleep if they were sick. 18% said they would watch t.v The poll included poll of 1,000 respondents. Construct a 90% confidence interval for the true percentage of adults who would watch t.v if they are home
Ho: M = E
Ha: M < E
Z = (mean1 - mean2)/standard error (SE) of difference between means
SEdiff = √(SEmean1^2 + SEmean2^2)
SEm = SD/√n
If only one SD is provided, you can use just that to determine SEdiff.
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability
related to the Z score.
If you have a question, it is much better to put it in as a separate post in <Post a New Question> rather than attaching it to a previous question, where it is more likely to be overlooked.
To conduct the hypothesis test, we need to define the null and alternative hypotheses. Let's assume the average entry-level mechanical engineering salary as "μm" and the average entry-level electrical engineering salary as "μe". The null hypothesis (Ho) states that the average mechanical engineering salary is not lower than the average electrical engineering salary (μm ≥ μe). The alternative hypothesis (Ha) argues that the average mechanical engineering salary is indeed lower than the average electrical engineering salary (μm < μe).
Ho: μm ≥ μe
Ha: μm < μe
Next, we can calculate the test statistic and the p-value to evaluate the hypothesis. We can use a two-sample independent t-test since we are comparing two independent groups. The formula for the test statistic is:
t = (x̄m - x̄e) / sqrt[(s^2m / nm) + (s^2e / ne)]
where:
x̄m = average salary of mechanical engineers
x̄e = average salary of electrical engineers
s^2m = variance of mechanical engineers' salaries
s^2e = variance of electrical engineers' salaries
nm = sample size of mechanical engineers
ne = sample size of electrical engineers
Plugging in the given values:
x̄m = $46,100
x̄e = $46,700
s^2m = $3,450^2 = $11,902,500
s^2e = $4,210^2 = $17,724,100
nm = 50
ne = 60
t = ($46,100 - $46,700) / sqrt[($11,902,500 / 50) + ($17,724,100 / 60)]
Now we can calculate the t-value (test statistic) and p-value using the calculated values:
t ≈ -0.782
df = nm + ne - 2 = 50 + 60 - 2 = 108 (degrees of freedom)
Using a t-table or a statistical software, we find that the p-value associated with a t-value of -0.782 and 108 degrees of freedom is approximately 0.2183.
Since the p-value (0.2183) is greater than the commonly used significance level of 0.05, we fail to reject the null hypothesis (Ho). The evidence does not provide sufficient support to conclude that the average entry-level mechanical engineering salary is lower than the average entry-level electrical engineering salary.
In conclusion, based on the given data, there is no significant evidence to suggest that the average entry-level mechanical engineering salary is lower than the average entry-level electrical engineering salary.