stats assignment

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Samples of 27 long-lasting batteries and 24 regular batteries were randomly collected in order to analyze the validity of the manufacturer's claim that their new long-lasting battery has an average life that is significantly longer than their competitor's regular battery. The life distributions for the sample of new long-lasting batteries and for the sample of 24 regular batteries was shown in the following pie charts. The average life of 27 long-lasting batteries was 49.56 with a standard deviation of 8.86, while The average life of 24 regular batteries was 40.79 with a standard deviation of 7.10.

The appropriate statistical test that should be used in this case is the two independent sample Student’s t-test since population standard deviations (σ) are unknown and sample standard deviations were used as estimates of population standard deviations. The significance level will be assumed to be 0.05. The null hypothesis is that the average life of the new long-lasting batteries is not longer than their competitor's regular battery. This hypothesis is tested against the claim that the average life of the new long-lasting batteries is longer than their competitor's regular battery. In other words, following set of hypotheses are being tested: vs

Next, a test statistic is calculated using the t-test formula: Correctly evaluating this equation results in a t-value of 3.87. In order to make a statistical decision, the test statistic (t= 3.87) must be compared to the corresponding critical values that depend on α and degrees of freedom (df). With α = 0.05 and , the critical value for this right tailed test is 1.677. Therefore, the null hypothesis can be rejected whenever . Since we have found the test statistic was 3.87, and it exceeds the critical value of 1.677 (). Thus, the null hypothesis is rejected and it can be concluded that the alternative hypothesis is true. There is sufficient evidence at the 0.05 level that average life of the new long-lasting batteries is longer than their competitor's regular batteries.

The distribution of the sample for the new batteries was slightly skewed to right. See the histogram below:

The distribution of the sample for the regular batteries was slightly skewed to left. See the histogram below:

Evaluating a larger sample size may provide more accurate results, but the overall outcome would probably be the same. An interesting problem is to test if both samples are from populations that are normally distributed.

Histogram

Frequency 30 40 50 60 70 More 0 6 9 9 3 0

Bin

Frequency

Histogram

Frequency 30 40 50 60 More 3 9 10 2 0

Bin

Frequency

Pie-Chart for Long-lasting Battery

"36" "37" "38" "40" "41" "44" "45" "48" "49" "50" "51" "53" "57" "58" "60" "63" "64" "65" 1 1 2 2 1 3 1 1 1 2 2 1 3 2 1 1 1 1

Pie-Chart for Regular Battery

"27" "29" "35" "36" "38" "39" "40" "41" "42" "44" "45" "48" "49" "50" "51" "55" 1 2 2 1 3 2 1 1 2 2 2 1 1 1 1 1

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