d CutEE Copy ▼H A0 .00Conditional FormatsteEEMerge & Center00 a0Format PainterFormatting- TableNumberClipboardFontAlignmentStyles27Gi110 parts made from alloy 1 and 46 parts made from alloy 2 were subjected to stress tests. 16 parts fromalloy 1 and 14 parts from alloy 2 did not pass the test. Can we reject the hypothesis that the proportion ofnonpassing parts from alloy 1 is at least as large as the proportion of nonpassing parts from alloy 2 at a-0.01?Assume independent samplesQuestion 1For the hypothesis stated above lin terms of alloy1- alloy2):Part A What is the decision rule? Fill in only one of the following statements.If the hypothesis is one tailed:If the hypothesis is twotailed:Reject Ho ifnrWhat is the test statistic?匚Part BQuestion 2Find the 90% confidence interval (in terms of alloy2-alloy!)Left Endpoint =Right EndpointRi

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Asked Apr 2, 2019
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110 parts made from alloy 1 and 46 parts made from alloy 2 were subjected to stress tests. 16 parts from
alloy 1 and 14 parts from alloy 2 did not pass the test. Can we reject the hypothesis that the proportion of
nonpassing parts from alloy 1 is at least as large as the proportion of nonpassing parts from alloy 2 at a-0.01?
Assume independent samples
Question 1
For the hypothesis stated above lin terms of alloy1- alloy2):
Part A What is the decision rule? Fill in only one of the following statements.
If the hypothesis is one tailed:
If the hypothesis is twotailed:
Reject Ho if
nr
What is the test statistic?
匚
Part B
Question 2
Find the 90% confidence interval (in terms of alloy2-alloy!)
Left Endpoint =
Right Endpoint
Ri
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d Cut EE Copy ▼ H A 0 .00Conditional Format ste EEMerge & Center 00 a0 Format Painter Formatting- Table Number Clipboard Font Alignment Styles 27 Gi 110 parts made from alloy 1 and 46 parts made from alloy 2 were subjected to stress tests. 16 parts from alloy 1 and 14 parts from alloy 2 did not pass the test. Can we reject the hypothesis that the proportion of nonpassing parts from alloy 1 is at least as large as the proportion of nonpassing parts from alloy 2 at a-0.01? Assume independent samples Question 1 For the hypothesis stated above lin terms of alloy1- alloy2): Part A What is the decision rule? Fill in only one of the following statements. If the hypothesis is one tailed: If the hypothesis is twotailed: Reject Ho if nr What is the test statistic? 匚 Part B Question 2 Find the 90% confidence interval (in terms of alloy2-alloy!) Left Endpoint = Right Endpoint Ri

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Expert Answer

Step 1

Question 1:

Conditions:

The conditions for the two proportion test for sample sizes n1 and n2 with sample proportion for the two samples being p1 and p2 respectively, are:

  • The data should be selected randomly.
  • The products n1p1 and n2p2, that is, the number of “successful cases” are greater than or equal to 10 for each sample.
  • The products n1 (1– p1) and n2 (1– p2), that is, the number of “failures” are greater than or equal to 10 for each sample.

Conditions for this problem:

It was found that 16 parts from alloy 1 did not pass the test out of 110 parts made and 14 parts from alloy 2 did not pass the test out of 46 parts made. It is checked whether the proportion of non-passing parts from alloy 1 is at least as large as the proportion of non-passing parts from alloy 2. The level of significance for the test is α=0.01.

Denote p1 and p2 as the proportion of parts of Alloy 1 that did not pass the test and proportion of parts of Alloy 2 that did not pass the test.

Therefore n1 = 110, p1 = 16/110 ≈ 0.145 and n2 = 46, p2 = 14/46 ≈ 0.304.

For alloy 1, number of parts that did not pass the test is 16 > 10.

For alloy 2, number of parts that did not pass the test is 14 > 10.

Hence, the conditions satisfied.  Therefore, we can use two-proportion z-test.

Hypotheses:

The aim is to check whether the proportion of non-passing parts from alloy 1 is at least as large as the proportion of non-passing parts from alloy 2.

The null hypothesis is:

H: p1p2 < 0, that is, the proportion of non-passing parts from alloy 1 is less than the proportion of non-passing parts from alloy 2.

The alternative hypothesis is:

H: p1p2 ≥ 0, that is, the proportion of non-passing parts from alloy 1 is at least as large as the proportion of non-passing parts from alloy 2.

Step 2

Part A:

The test is a one tailed test,

Decision rule:

  • If the test statistic is greater that the critical value (zα), reject the null hypothesis.
  • Otherwise fail to reject the null hypothesis.
Step 3

Part B:

Test statistic:

...
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