Answer:
The manufacturer's claim is not supported
Step-by-step explanation:
The time duration the battery of the foldable drone is said to last, μ = 4 hours
The number of drones that were tested, n = 10 drones
The sample mean,
= 4.2 hours
The standard deviation, s = 0.4 hours
The hypothesis test level of significance = 0.5
The null hypothesis, H₀; μ = 4
The alternative hypothesis, Hₐ; μ ≠ 4
The test statistic is given as follows;
![t=\dfrac{\bar{x}-\mu }{\dfrac{s }{\sqrt{n}}}](https://tex.z-dn.net/?f=t%3D%5Cdfrac%7B%5Cbar%7Bx%7D-%5Cmu%20%7D%7B%5Cdfrac%7Bs%20%7D%7B%5Csqrt%7Bn%7D%7D%7D)
We get;
![The \ test \ statistic, \ t =\dfrac{4.2 - 4}{\dfrac{0.4}{\sqrt{10} } } \approx 1.58113883008](https://tex.z-dn.net/?f=The%20%5C%20test%20%5C%20%20statistic%2C%20%5C%20%20t%20%3D%5Cdfrac%7B4.2%20-%204%7D%7B%5Cdfrac%7B0.4%7D%7B%5Csqrt%7B10%7D%20%7D%20%7D%20%20%5Capprox%20%201.58113883008)
Therefore, the test statistic, t ≈ 1.58
The degrees of freedom, d. f. = n - 1
For n = 10, we have;
The degrees of freedom, d. f. = 10 - 1 = 9
From the t-table at 0.5 level of significance, the critical-t = 0.7
Given that the test statistic is larger than the critical-t, we reject the null hypothesis and there is enough statistical evidence to suggest that the manufacturer claim is not supported and that the mean is not 4 hours as claimed.