AJ Davis Department Store Project Part B: Hypothesis Testing and Confidence Intervals A. The average (mean) annual income was less than $50,000 • Null Hypothesis is the average annual income is ≥ to $50,000. o Ho: µ ≥ 50,000 • Alternate Hypothesis is the average annual income is < than $50,000. o Ha: µ < 50,000 • Analysis Plan significance level is: a = 0.05 • n > 30 the z test was used to test the hypothesis • Alternative Hypothesis Ha: µ ≥ 50,000, this means the test is a one tailed z test. Critical Value and Decision Rule • C.V: a = 0.05 the lower tailed z test is 1.645 • D.R: reject Ho if z – statistic is -1.645 Sample Z using Minitab: • Income …show more content…
viation = 5.103 N Mean SE Mean 95% CI Z P 50 13.000 0.722 (11.586, 14.414) 0.86
So, we should reject the null hypothesis H0. At a 0.05 level of significance level, we conclude that there is a significant difference between the average height for females and the average height for the males.
Kyle Davis drove in a career-high five runs and the West Virginia University offense came alive a day after being shutout to pound Tulane 18-5 on Sunday afternoon in the series finale.
a. What are the estimated sales for the Bryne store, which has four competitors, a
The Cleveland Browns finally dove into the free agent market by signing linebacker Demario Davis. The two parties agreed to a two year, eight million dollar contract which benefits both sides. Although Davis isn’t a big name free agent, he brings a positive attitude and no off-field baggage.
The most recent case that I have researched it the Troy Davis case. In this case Troy Davis was accused of killing Officer Mark Allen MacPhail. It all began around midnight on Friday, August 18, 1989, a teenager named Michael Cooper was shot in the jaw as he and his friends were driving away from a pool party they attended in Cloverdale area of Savannah, Georgia. Approximately, an hour later in the early morning of Saturday, August 19, 1989, there was a group of young men that were at a pool hall by the name of Charlie Brown’s pool hall. Charlie Brown’s was located across the street from Greyhound bus station and Burger King Restaurant. A homeless man named Larry Young went into the convenience store next to the pool hall to purchase a beer. When he exited with his beer in his hand he was greeted by Sylvester “Redd” Coles who was wearing a yellow
The 95% confidence interval for the population mean is 66,438 to 80,241. This means that there is a 95% confidence that this interval has the population mean.
This means the data was statistically significant and we can reject the null hypothesis. The alternative hypothesis states that as an individual ages after the age of 18, their total family income will increase. A two way table test for homogeneity for a characteristic distribution was performed to analyze the data which included two populations, 18-45 and 45-96 age groups. Individuals between the ages of 45-96 have a higher total family income in the income brackets of $0-$60,000 and $60,000-$250,000. However, a Type I Error may have occurred where the null hypothesis was rejected, but in fact was true. This means that individuals between the ages of 18-45 do have a total family income greater than or equal to the individuals between the ages of 45-96. A consequence of this this error could be that individuals between the ages of 18-45 going to jail for tax fraud. A Type II Error on the other hand, would mean that we failed to reject the null hypothesis when the null hypothesis is in fact false. This means that individual's total family income between the ages of 18-45 is not greater than or equal to the total family income of individuals between the ages of 45-96. A consequence of this could be the government believing that individuals in the 18-45 age range make more money than what they actually do thus failing to allot the necessary financial and government
Nevertheless, if a rejection of the null hypothesis occurs, then insufficient evidence proposes that H1 exists as proofs (Mirabella, 2011). Further concluding the lower-tail test identifies a p-value of 0.002, therefore, the decision remains; reject the null hypothesis. According to Mirabella (2011), the confidence interval is another way to acquire the sample mean. To organize this, just utilize the mean added to or minus a margin of error. Furthermore, the margin of error or sampling error is merely the difference between the results and the truth (Mirabella, 2011). Therefore, the sampling error necessity determined is vital in order to develop a sample mean. Early units have taught us, the Z score times the standard deviation divided by the square root of the sample size. Therefore, the Z score remains known as plus/minus of the level of confidence based on the data in the normal distribution.
From this analytic calculation it is clear that both the null and alternative hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean is too small. For this analysis, the significance level is 0.01. The test method is a one sample t-test.
Therefore, two-tail hypothesis testing has applied to test the effect of both variables, the null and alternative hypothesis are below:
There are seven steps that will be used within this paper to test a hypothesis. These steps include the following; Step 1: which is stating the null hypothesis, stating the research hypothesis, identifying the target population and sample population, identifying the independent variable and dependent variable. Step 2: establishing the level of significance. Step 3: selecting a one-tailed or two-tailed test. Step 4: conducting the test and excel and providing the results as an excel output. Step 5: calculating the degree of freedom. Step 6: stating the critical value to exceed by the calculated test statistic. Lastly, Step 7: comparing the calculated test statistic and to the level of significance and making a decision about the results. The following steps will be explained in further detail below.
Remember the pictures for the critical score approach from the last section? I’ve reproduced them here. The rejection region on each (in blue) shows the rejection region of the test. If zsam (or tsam) ends up in this range, it’s a “more extreme” or “weirder” value than the critical z (or t) score, and so we reject the null hypothesis. In brief:
Since the population standard deviation is not known and in our test the number of observed data (n) is more than 30, we do not qualify for using t-statistic and henceforth we use z statistic for our analysis.
Z = the standard normal deviate set at 1.96 which corresponds to the 95 % confidence level.
primary data. Statistical Tools Used : Z – test is used as a test to verify the different objectives