A cell phone manufacturer claims that the average battery life of its newest flagship smartphone is exactly 20 hours. Javier believes the population mean battery life is less than 20 hours. He tests this claim by selecting a random sample of 33 phones of this model. Javier found that the sample mean battery life is 19.5 hours with a sample standard deviation of 1.9 hours. The test statistic t for a hypothesis test of H0:μ=20 versus Ha:μ<20 is t≈−1.51 with 32 degrees of freedom. If 0.05<p-value<0.10 and the level of significance is α=0.05, which of the following statements are accurate for this hypothesis test to evaluate the claim that the true population mean battery life of the smartphone is less than 20hours?Select all that apply:A) Reject the null hypothesis that the true population mean battery life of the smartphone is equal to 20 hours.B) Fail to reject the null hypothesis that the true population mean battery life of the smartphone is equal to 20 hours.C) There is not enough evidence at the α=0.05 level of significance to suggest that the true population mean battery life of the smartphone is less than 20 hours.D) There is enough evidence at the α=0.05 level of significance to support the claim that the true population mean battery life of the smartphone is not equal to 20 hours.

Question
Asked Jun 13, 2019
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A cell phone manufacturer claims that the average battery life of its newest flagship smartphone is exactly 20 hours. Javier believes the population mean battery life is less than 20 hours. He tests this claim by selecting a random sample of 33 phones of this model. Javier found that the sample mean battery life is 19.5 hours with a sample standard deviation of 1.9 hours. The test statistic t for a hypothesis test of H0:μ=20 versus Ha:μ<20 is t≈−1.51 with 32 degrees of freedom. If 0.05<p-value<0.10 and the level of significance is α=0.05, which of the following statements are accurate for this hypothesis test to evaluate the claim that the true population mean battery life of the smartphone is less than 20hours?

Select all that apply:

A) Reject the null hypothesis that the true population mean battery life of the smartphone is equal to 20 hours.

B) Fail to reject the null hypothesis that the true population mean battery life of the smartphone is equal to 20 hours.

C) There is not enough evidence at the α=0.05 level of significance to suggest that the true population mean battery life of the smartphone is less than 20 hours.

D) There is enough evidence at the α=0.05 level of significance to support the claim that the true population mean battery life of the smartphone is not equal to 20 hours.

 

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Expert Answer

Step 1

Given 
Null Hypothesis Ho : µ = 20
Alternative Hypothesis Ha : µ < 20

Sample size n = 3
Sample mean = 19.5 hours
Sample standard deviation = 1.9 hours
Sample statistic t = -1.51 
degree of freedom = n-1 = 32
level of significance...

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