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Nostrana [21]
3 years ago
15

The manufacturer of an airport baggage scanning machine claims it can handle an average of 560 bags per hour. (a-1) At α = .05 i

n a left-tailed test, would a sample of 16 randomly chosen hours with a mean of 538 and a standard deviation of 50 indicate that the manufacturer’s claim is overstated? Choose the appropriate hypothesis.
Mathematics
1 answer:
ioda3 years ago
6 0

Answer:

The calculated value t = 1.76 < 2.131 at 0.05 level of significance

Null hypothesis is accepted

The manufacturer’s claim is greater than 560 bags per hour

Step-by-step explanation:

<u><em>Explanation</em></u>:-

Given sample size 'n' =16

Given the manufacturer of an airport baggage scanning machine claims it can handle an average of 560 bags per hour.

mean of the Population 'μ' = 560

Mean of the sample Χ⁻ = 538

sample standard deviation' S' = 50

<em><u>Null hypothesis</u></em><em>:H₀:μ > 560</em>

<em><u>Alternative Hypothesis</u></em><em>:H₁ : :μ < 560 (left tailed test)</em>

<em>Test statistic</em>

   t = \frac{x^{-}-mean }{\frac{S}{\sqrt{n} } }

  t = \frac{538-560 }{\frac{50}{\sqrt{16} } } = -1.76

|t| = |-1.76| = 1.76

<em>Degrees of freedom </em>

<em>γ = n-1 =16-1 =15</em>

t_{\frac{\alpha }{2} } = t_{\frac{0.05}{2} } =t_{0.025} =2.131

<em><u>Conclusion</u></em>:-

The calculated value t = 1.76 < 2.131 at 0.05 level of significance

Null hypothesis is accepted

The manufacturer’s claim is greater than 560 bags per hour

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3 years ago
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Hence, the probability that a battery will last more than 19 hours is 0.0668.

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