The desired percentage of SiO₂ in a certain type of aluminous cement is 5.5. To test whether the true average percentage

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The Desired Percentage Of Sio In A Certain Type Of Aluminous Cement Is 5 5 To Test Whether The True Average Percentage 1 (59.37 KiB) Viewed 81 times

The desired percentage of SiO₂ in a certain type of aluminous cement is 5.5. To test whether the true average percentage is 5.5 for a particular production facility, 16 independently obtained samples are analyzed. Suppose that the percentage of Si0, in a sample is normally distributed with a = 0.32 and that x = 5.21. (Use a = 0.05.) (a) Does this indicate conclusively that the true average percentage differs from 5.5? State the appropriate null and alternative hypotheses. ⒸH₁: #= 5.5 H₂₁:μ = 5.5 OHH = 5.5 H₂H< 5.5 ⒸH₁: = 5.5 HP> 5.5 ⒸH₂² # = 5.5 HAZ 5.5 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your p value to four decimal places.) 2 = P-value= State the conclusion in the problem context. O Do not reject the null hypothesis. There is not sufficient evidence to conclude that the true average percentage differs from the desired percentage. O Reject the null hypothesis. There is sufficient evidence to conclude that the true average percentage differs from the desired percentage.. O Reject the null hypothesis. There is not sufficient evidence to conclude that the true average percentage differs from the desired percentage. O Do not reject the null hypothesis. There is sufficient evidence to conclude that the true average percentage differs from the desired percentage. (b) If the true average percentage is = 5.6 and a level a= 0.01 test based on n = 16 is used, what is the probability of detecting this departure from Ho? (Round your answer to four decimal places.) (c) What value of n is required to satisfy a = 0.01 and 3(5.6)= 0.017 (Round your answer up to the next whole number.) n= samples