Coursework of Statistics for Business Essay Example

Statistics for Business Individual Assignment

Course: STA101 – Statistics for Business

Department:

2^nd June, 2017

Question 1

1. The frequency distribution table

The number of bins was chosen in line with Sturges’ number of bins rule. According to the rule,
(Scott, 2009, p. 48).

Given that the number of Noodles and Company restaurants is 74, number of classes is
. Number of class intervals is approximately 7. Sturges rule is also applied in obtaining the approximate value of the size of class interval. The rule is tabulated below:

2. Histogram

The histogram is right skewed with longer tail to the right. This means that the mean is greater than the median effectively giving the right skewed distribution. The right skewed distribution further shows that few customers have high average spending. On the other hand, most customers spend very little in the 74 Noodles & Company restaurants. Furthermore the histogram shows that the distribution is unimodal with a single peak value.

3. Larger number of bins

The visual impression did not change when the number of bins was increased. It is apparent that the distribution is right skewed with a longer tail stretching to the right. Moreover, the distribution is unimodal with a single peak value.

Question 2

1. Probability that a viewer is aged 18-34

2. Probability that a viewer prefers watching TV videos

3. Percentage of viewers who are 18-34 and prefer watching user-created videos

4. Percentage of viewers aged 18-34 who prefer watching user-created videos

5. Percentage of viewers who are 35-54 or prefer user created videos

Question 3

1. The mean, mode and median for each quiz has been displayed on the table below

2. The mean and median are nearly the same across the quizzes. Even though the mode is slightly low, the data seem to have a normal distribution. If the distribution were perfectly symmetrical, then the mean, mode, and median would have a common a value.

3. Quiz 1, 2, 3 and 4 are slightly skewed, An appropriate measure of central tendency for the skewed distribution is the median. In a skewed data, mean is usually dragged in the direction of skewness hence median ought to be used because it is unaffected by extreme values.

4. Quiz 2 is nearly symmetrical since it has a skewness that lies between -0.5 and 0.5. Quiz 1 and 3 are slightly positively skewed while quiz 4 is negatively skewed.

5. In exam 1 and 2 students performed approximately the same with a mean of 72. Student’s performance improved in exam 3 and 4 with a higher mean of 76 in both exams. In summary, performance is improving across the examination given the nature of the rising mean and median.

Question 4

a. H0: μ = 200 versus H1: μ ≠ 200, α = .025,
= 203, s = 8, n = 16

We will reject the
and accept the

given that the

b. H0: μ ≥ 200 versus H1: μ < 200, α = .05,
= 198, s = 5, n = 25

We will reject the
and accept the

given that the

c. H0: μ ≤ 200 versus H1: μ > 200, α = .05,
= 205, s = 8, n = 36

We will fail to reject the

given that the

Question 5

1. 95% confidence interval for the mean score

The confidence interval means that we are 95% confident that exam scores lies between
.

The confidence interval means that we are 95% confident that exam scores lies between .

The confidence interval implies that we are 95% confident that exam scores lies between .

2. The scores overlap with exam 2 having a greater confidence interval. By comparing confidence interval, it is apparent that more students scored between
   . Students performed well in exam 2 compared with exam 1 and exam 3.

Question 6

1. Probability of producing at least 230,000 barels

2. Between 232,000 and 239,000 barrels

3. Less than 239,000 barrels?

4. Less than 245,000 barrels?

5. More than 225,000 barrels?

Reference

Scott, David 2009, Multivariate Density Estimation: Theory, Estimation, and Visualization, New York, John Wiley & Sons.