MATH SOLVE

5 months ago

Q:
# The manufacturer of an airport baggage scanning machine claims it can handle an average of 530 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 510 and a standard deviation of 50 indicate that the manufacturer’s claim is overstated? Choose the appropriate hypothesis.

Accepted Solution

A:

Answer:(a) H1: μ < 530. Reject H1 if tcalc > –1.753(b) t calc = –1.6. There is not enough evidence to reject the manufacturer’s claim. Step-by-step explanation:We are given that the manufacturer of an airport baggage scanning machine claims it can handle an average of 530 bags per hour. A sample of 16 randomly chosen hours with a mean of 510 and a standard deviation of 50 is given.Let [tex]\mu[/tex] = average bags an airport baggage scanning machine can handleSo, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \geq[/tex] 530 bags {means that an airport baggage scanning machine can handle an average of more than or equal to 530 bags per hour}Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 530 bags {means that an airport baggage scanning machine can handle an average of less than 530 bags per hour}The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation; T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]where, [tex]\bar X[/tex] = sample mean = 510 s = sample standard deviation = 50 n = sample of hours = 16So, test statistics = [tex]\frac{510-530}{\frac{50}{\sqrt{16} } }[/tex] ~ [tex]t_1_5[/tex] = -1.60The value of t test statistics is -1.60.Now, at 0.05 significance level the t table gives critical value of -1.753 at 15 degree of freedom for left-tailed test. Since our test statistics is more than the critical values of t as -1.60 > -1.753, so we have insufficient evidence to reject our null hypothesis as it will not in the rejection region due to which we fail to reject our null hypothesis.Therefore, we conclude that an airport baggage scanning machine can handle an average of more than or equal to 530 bags per hour.