Question

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

Answer 1

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

Explanation:

Explanation:-

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

Null hypothesis:H₀:μ > 560

Alternative Hypothesis:H₁ : :μ < 560 (left tailed test)

Test statistic

`t = (x^(-)-mean )/((S)/(√(n) ) )`

`t = (538-560 )/((50)/(√(16) ) ) = -1.76`

|t| = |-1.76| = 1.76

Degrees of freedom

γ = n-1 =16-1 =15

`t_{(\alpha )/(2) } = t_{(0.05)/(2) } =t_(0.025) =2.131`

Conclusion:-

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