A consumer electronics firm has developed a new type of remote control button that is designed to operate longer before becoming intermittent. A random sample of 35 of the new buttons is selected and each is tested in continuous operation until becoming intermittent. The resulting lifetimes are found to have a sample mean of = 1,241.2 hours and a sample standard deviation of s = 110.8. Assuming normality of the population, the p-value for testing H0 versus Ha can be calculated to be. 0174. (a) Determine whether H0 would be rejected at each of α =.10, α =.05, α =.01, and α =.001.

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Mathematics

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11 September, 09:14

A consumer electronics firm has developed a new type of remote control button that is designed to operate longer before becoming intermittent. A random sample of 35 of the new buttons is selected and each is tested in continuous operation until becoming intermittent. The resulting lifetimes are found to have a sample mean of = 1,241.2 hours and a sample standard deviation of s = 110.8. Assuming normality of the population, the p-value for testing H0 versus Ha can be calculated to be. 0174. (a) Determine whether H0 would be rejected at each of α =.10, α =.05, α =.01, and α =.001.

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Luca Benton · Answer 1

At 0.10 significance level, reject H0

At 0.05 significance level, reject H0

At 0.01 significance level, fail to reject H0

At 0.001 significance level, fail to reject H0

Step-by-step explanation:

The null hypothesis is rejected if the p-value is less than or equal to the significance level.

Fail to reject the null hypothesis if the p-value is greater than the significance level.

At 0.1 and 0.05 significance level, the null hypothesis is rejected because the p-value (0.0174) is less than the significance levels.

At 0.01 and 0.001 significance level, fail to reject the null hypothesis because the p-value (0.0174) is greater than the significance levels.