Phone Plastic T-Test

Running head: PHONE PLASTIC T-TEST

Phone Plastic t-Test

Lisa Boyle

University of Phoenix

Cell Phone Plastic t-Test

Research Problem Question and Purpose

The research problem is, is there a there a difference between cell phones that are heated and unheated that would cause damage in temperature over 120 degrees? The purpose is to gain insight about the company’s cell phones.

There are fifteen observations for each of the two batches of cell phones. By reducing the number of data to the minimum needed to describe the sample, eliminates the redundancy, and reduces time and costs associated with another data set that may be in the thousands. This is called descriptive statistics because the mass of raw data is transformed into a meaningful form (Lind, 2004). This can be accomplished by describing the central data point, the spread, and the shape (University of Phoenix, 2008). In this particular test, the interest rests in the cell phones’ crushing resistance. The measured variables are in pounds per square inch (PSI). The resistance of the first batch was recorded as: 50, 36, 34, 45, 56, 42, 53, 25, 65, 33, 40, 42, 39, 43, 42. The second batch of 15 were measured after being heated to 120 degrees Fahrenheit for six hours as: 43, 44, 51, 40, 29, 49, 39, 59, 43, 48, 67, 44, 46, 54, 64 (University of Phoenix, 2008). In addition, for the decision-maker to avoid confusion and error, the right numbers must be chosen.

The mean of the unheated cell phones is 43 and the mean of the heated cell phones is 48.

The mean is the equality of all observations. The arithmetic mean is a widely used measure of location and has several important properties: every set of interval or ratio-level data has a mean, and ratio-level data include such data as ages, incomes, and weights, with the distance between number being constant. All the values are included in computing the mean. A set of data has only one mean. The mean is unique. Lastly, the sum of the deviation of each value form the mean will always be zero. Expressed symbolically: в?'(X- X) = 0 (Lind, p. 59).

The median of the unheated cell phones is 42 for the unheated and 46 for the heated cell phones. It is described as the midpoint of values after they have been ordered in either ascending or descending order. Ex:

Unheated cell phones vs. Heated cell phones

65 67

56 64

53 59

50 54

45 51

43 49

42 48

42 Ð'«Median 46 Ð'«Median

42 44

40 44

39 43

36 43

34 40

33 39

25 29

The mode will describe that 42 of the unheated and 43 of the heated cell phones, which are the highest frequency of occurrence. This is also used as central tendency for attribute (non-numeric) data, such as, nominal and ordinal (Lind, 2004).

The standard deviation is 9.96 of the unheated and 9.91 of the heated cell phones, which is a result of the square root of the variance (Lind, 2004, p. 74).

The range is the difference between the highest and the lowest. Unheated equals 65-25= 40, and for the heated cell phones equals 67-29=38.

The kurtosis for the unheated is 0.70 and for the heated cell phones is 0.26, which is the measure of the peak. In other words, it describes how peaked is the data.

Skewness means how one-sided is the data. The skewness for the unheated is 0.52 and for the heated cell phones is 0.34 is the degree of asymmetry about the mean.

Two-Sample of Tests of Hypothesis

State H0 and H1.

H0: There is a difference in the proportion of unheated cell phones and heated cell phones when exposed to temperatures over 120 degrees.

H1: There is not a difference in the proportion of unheated cell phones and heated cell phones when exposed to temperatures over 120 degrees.

The level of significance is 0.05 and the t-test is the test statistic to compare two means because the samples contain fewer than 30 observations.

As the test is completed, the company’s decision is not to reject the null hypothesis, because t is equal to -1.38 and falls in the region between -2.048 and 2.048. The conclusion is there is a difference in the proportion of unheated cell phones and heated cell phones when exposed to temperatures over 120 degrees. The two-tailed p-value is 0.1791, which is larger than the significance level of 0.05. The conclusion is not to reject the null hypothesis.

Descriptive statistics

Unheated

count 15

mean 43.00

sample variance 99.14

sample standard deviation 9.96

minimum 25

maximum 65

range 40

sum 645.00

sum of squares 29,123.00

deviation sum of squares (SSX) 1,388.00

confidence interval 95.% lower 37.49

confidence

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