A manufacturer of a laserbased inspection equipment claims t

A manufacturer of a laser-based inspection equipment claims the its product can inspect on average 30 solder joints per second when the joints are spaced 1mm apart. The equipment was tested by a potential buyer on 45 printed circuit boards (PCB). The average number of solder joints per second for the sample was 27.3 with a standard deviation of 2.2.

a.) Do think that there is enough evidence to support the manufacturer\'s claim? Conduct the appropriate hypothesis test to support your conclusion. (alpha = 0.05)

b.) Calculate a 95% confidence interval of the mean number of PCB inspected per second. Explain the meaning of the confidence interval.

c.) Calculate a 90% confidence interval of the mean number of PCB inspected per second. Explain the meaning of the confidence interval.

d.) What is the effect of the confidence level on the confidence intervals on part (b) and (c)?

Solution

First set up null and alternate hypothesis as

H0: Mu = 30

Ha: mu <30

Left railed hypothesis test.

Sample mean = 27.3

Unbiased standard deviation = 2.2

Sample size = 45

std error = 2.2/rt 45 = 0.328

Population size = (left blank)

Mean of the population = 30

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t value = -.0.7/0.328 = -2.134

Degrees of freedom = 44

p value for left = 0.019

The result is significant at 0.01 level.

b) confidence interval 95% = (26.66, 27.94)

(margin of error = 1.96*se = 0.64)

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c) conf int 90% = (26.76 , 27.84)

Margin of error = 0.54

d) As population mean 30 is not contained in both the intervals, we decline null hypothesis at 90% and also 95%