Question

A certain type of battery produced by Omni Consumer Products has historically had an average lifespan of no more than 87 hours. Omni believes that an improved production process will be able to increase the lifespan of this battery, but it needs to do some testing before it can conclude anything. Researchers gathered a sample of 36 batteries and found the sample mean lifespan was 88.5 hours, with a standard deviation of 9.1 hours

Perform a hypothesis test at the α = 0.05 level of significance by filling in the blanks below. Type the correct symbols, words, and numbers. Type < for "less than," > for "greater than", = for "equal to", etc. as needed.

1).Define the hypotheses.

H₀: μ ≤

H₁: μ > 87

2). Calculate the test statistic. Take all calculations to three (3) decimal places; enter your answer to two (2) decimal places.

t =

3). Determine the rejection (or critical) region.

All t >

4). Make a conclusion iin the context of the problem. Enter one of the terms in parentheses for each blank in this section.

Omni will  (reject/fail to reject) the null hypothesis. The company  (can/cannot) conclude that the mean lifespan of the battery has increased.

Answer 1

Given that, sample size (n) = 36

sample mean = 88.5 hours and

standard deviation = 9.1 hours

1)The null and alternative hypotheses are,

H0 : μ ≤ 87

Ha : μ > 87

2) Test statistic is,

=> t = 0.99

3) t-critical value at significance level of 0.05 with degrees of freedom = 36 - 1 = 35 is, t_{​​​​​​crit} = 1.69

Rejection region : t > 1.69

4) Since, t = 0.99 < 1.69, we fail to reject H0.

Conclusion : Omini will fail to reject the null hypothesis. The company cannot conclude that the mean lifespan of the battery has increased.

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