A legal case rested on whether a patent witness\' signature was written on top o

Question

A legal case rested on whether a patent witness' signature was written on top of key text in a notebook or under the key text. The zinc measurements for three notebook locations-on a text line, on a witness line, and on the intersection of th witness and text line-are provided in the table below. Complete pans a through d. Use a test (at alpha = 0.02) to compare the mean zinc measurement for the text line with the mean for the intersection. Let mu_1 represent the mean zinc measurement for the text line, let mu_2 represent the mean zinc measurement for the signature of a patent witness, and let mu_3 represent the mean zinc measurement for the intersection line. Select the correct hypotheses below. H_0: mu_1 - mu_3 = 0, H_1: mu_1 - mu_3 > 0 H_0:mu_1 - mu_3 = 0, H_1:mu_1 - mu_3 0 Find the test statistic. (Round to two decimal places as needed.) Find the critical value(s). (Use a comma to separate answers as needed. Round to three decimal places as needed.) Find the p-value. (Round to four decimal places as needed.) Choose the correct conclusion below. Assume alpha = 0.02. Reject H_0. There is sufficient evidence that the mean measurements of zinc for the text line and intersection line are different Do not reject H_0. There is insufficient evidence that mean measurements of zinc for the text line and the the intersection line are different Do not reject H_0. There is sufficient evidence that the mean measurements of zinc for the text line and the intersection line are different Reject H_0. There is insufficient evidence that the mean measurements of zinc for the text line and the intersection line are different Use a test (at alpha = 0.02) to compare the mean zinc measurement for the witness line with the mean for the intersection. Select the correct hypotheses below. H_0: mu_1 - mu_2 = 0, H_1: mu_1 - mu_3 0 H_0mu_2-mu_3 = 0, H_1: mu_2 - mu_3 0 Find the test statistic. (Round to two decimal places as needed.) Find the critical value(s). (Use a comma to separate answers as needed. Round to three decimal places as needed.) Find the p-value. (Round to four decimal places as needed.) Choose the correct conclusion below. Assume alpha = 0.02. Do not reject H_0. There is insufficient evidence that the mean measurements of zinc for the witness line and the intersection line are different. Reject H_0. There is sufficient evidence that line mean measurements of zinc for the witness line and the intersection line are different. Do not reject H_0. There is sufficient evidence that the mean measurements of zinc for the witness line and the intersection line are different. Reject H_0. There is insufficient evidence that the mean measurements of zinc for the witness line and the intersection line are different. From the results in parts a and b, what can you infer about the mean zinc measurements at the three notebook locations? The mean zinc measurement at the intersection is not different from the mean zinc measurement at the text line and is not different from the mean zinc measurement at the witness line. The mean zinc measurement at the intersection is different from the mean zinc measurement at the text line and is not different from the mean zinc measurement at the witness line. The mean zinc measurement at the intersection is different from the mean zinc measurement at the text line and is different from the mean zinc measurement at the witness line. The mean zinc measurement at the intersection is not different from the mean zinc measurement at the text line and is different from the mean zinc measurement at the witness line. What assumptions are required for the inferences to be valid? The three samples are randomly selected in an independent manner from the three target populations. All three sampled populations have distributions that are approximately normal. All three population variances are equal. None of the three population variances are equal. The three sample sizes are approximately equal.

Explanation / Answer

Let mu1 represent the mean zinc measurement for the text line.

mu2 represent the mean zinc measurement for the signature of a parent witness.

mu3 represent the mean zinc measurement for the intersection line.

Assume alpha = level of significance = 0.02

We have to test the hypothesis that,

H0 : mu1 - mu3 =0 Vs H1 : mu1 - mu3 0

Option B) is correct.

Assuming equal variances.

We can find the test statistic value by using EXCEL.

steps :

Enter the data in EXCEL sheet --> Data --> Data Analysis --> t-test: Two-Sample Assuming Equal Variances --> ok --> Variable 1 Range : select text line range --> Variable 2 Range : select intersection line range --> Hypothesized mean difference is 0 --> Alpha : 0.02 --> Output Range : select one empty cell --> ok

Test statistic t = 1.26

Critical value is 3.143.

And P-value = 0.2530

P-value > alpha

Accept H0 at 2% level of significance.

Conclusion : There is insufficient evidence to say that the mean measurement of text line is equal to mean measurement of intersection.

The mean zinc measurement at the intersection is not different from the mean zinc measurement at the text line and is not different from the mean zinc measurement at the witness line.

Assumptions :

1) All three sampled populations have distributions that are approximately normal.

2) All three population variances are equal.

3) The three samples are randomly selected in an independent manner from the three target populations.

t-Test: Two-Sample Assuming Equal Variances Variable 1 Variable 2 Mean 0.396333333 0.3482 Variance 0.004196333 0.0019772 Observations 3 5 Pooled Variance 0.002716911 Hypothesized Mean Difference 0 df 6 t Stat 1.26447096 P(T<=t) one-tail 0.126478719 t Critical one-tail 2.612241845 P(T<=t) two-tail 0.252957438 t Critical two-tail 3.142668403

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