(a) Do the data provide evidence that high temperature increases the hardness of 5% copper alloys, on average? What is the distribution of the test statistic under the null hypothesis and the exact p-value? O t-distribution with df = 18; p-value = 0.0862 O t-distribution with df = 9; p-value = 0.00712 O t-distribution with df = 9; p-value = 0.00356 O t-distribution with df = 18; p-value = 0.9569 O t-distribution with df = 18; p-value = 0.0431 (b) What is the BEST CORRESPONDING 95% confidence interval or bound for Hd, where d = xH5 - XH5HT?

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Titanium alloys have very high hardness. Adding small amounts of copper tends to improve their properties, such as
hardness. In order to evaluate the effect of copper addition on hardness of titanium alloys, 10 random casts with 5%
copper were made in an argon-arc melting furnace. The Rockwell hardness was determined for each of the casts. Then,
the casts were subjected to high temperature (HT) and hardness was determined again in the second row. Assume
hardness follows a normal distribution. Use the data below to answer the next three questions.
248 246 245 251 248 250 247 246 243 244
HARD5
HARD5HT 250 247 246 251 251 253 248 246 249 247
(a) Do the data provide evidence that high temperature increases the hardness of 5% copper alloys, on average? What is
the distribution of the test statistic under the null hypothesis and the exact p-value?
O t-distribution with df = 18; p-value = 0.0862
O t-distribution with df = 9; p-value = 0.00712
O t-distribution with df = 9; p-value = 0.00356
O t-distribution with df = 18; p-value = 0.9569
O t-distribution with df = 18; p-value = 0.0431
(b) What is the BEST CORRESPONDING 95% confidence interval or bound for Hd, where d = xH5 - XH5HT?
О (3.306, о0)
O (-3.306, -0.694)
O (-00, -0.942)
O (-3.058, ∞)
О (00, -0.694)
Transcribed Image Text:Titanium alloys have very high hardness. Adding small amounts of copper tends to improve their properties, such as hardness. In order to evaluate the effect of copper addition on hardness of titanium alloys, 10 random casts with 5% copper were made in an argon-arc melting furnace. The Rockwell hardness was determined for each of the casts. Then, the casts were subjected to high temperature (HT) and hardness was determined again in the second row. Assume hardness follows a normal distribution. Use the data below to answer the next three questions. 248 246 245 251 248 250 247 246 243 244 HARD5 HARD5HT 250 247 246 251 251 253 248 246 249 247 (a) Do the data provide evidence that high temperature increases the hardness of 5% copper alloys, on average? What is the distribution of the test statistic under the null hypothesis and the exact p-value? O t-distribution with df = 18; p-value = 0.0862 O t-distribution with df = 9; p-value = 0.00712 O t-distribution with df = 9; p-value = 0.00356 O t-distribution with df = 18; p-value = 0.9569 O t-distribution with df = 18; p-value = 0.0431 (b) What is the BEST CORRESPONDING 95% confidence interval or bound for Hd, where d = xH5 - XH5HT? О (3.306, о0) O (-3.306, -0.694) O (-00, -0.942) O (-3.058, ∞) О (00, -0.694)
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