Question

10,8,10,9,11,10,13,8,9,10,6,9,
7,11,12,9,10,12,9,10,10,10,11,
9,10,9,8,6,11,6,10,9,10,9,8,9,
11,12,10,0,11,12,12,9,7,8,10,9

Current technology uses​ high-resolution X-rays and lasers for inspection of​ solder-joint defects on printed circuit boards​ (PCBs). A particular manufacturer of​ laser-based inspection equipment claims that its product can inspect on average at least 9 solder joints per second when the joints are spaced 0.1 inch apart. The equipment was tested by a potential buyer on 48 different PCBs. In each​ case, the equipment was operated for exactly 1 second. The numbers of solder joints inspected on each run are shown in the accompanying data table.

H0​:μ=9

Ha​:μ<9

Conduct the hypothesis test you described above

and interpret the​ test's results in the context of this exercise. Use α=0.05. Calculate the value of the test statistic.

Z = _______ (Round to two decimal places as​ needed.)

P = _______ (Round to three decimal places as​ needed.)

Answer 1

Solution;-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u > 9.0
Alternative hypothesis: u < 9.0

Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample z-test.

Analyze sample data. Using sample data, we compute the standard error (SE), z statistic test statistic (z).

SE = s / sqrt(n)

S.E = 0.30726

z = (x - u) / SE

z = 1.15

where s is the standard deviation of the sample, x is the sample mean, u is the hypothesized population mean, and n is the sample size.

The observed sample mean produced a z statistic test statistic of 1.15.

Thus the P-value in this analysis is 0.875

Interpret results. Since the P-value (0.875) is greater than the significance level (0.05), we cannot reject the null hypothesis.

From the above test we have sufficient evidence in the favor of the claim that that its product can inspect on average at least 9 solder joints per second when the joints are spaced 0.1 inch apart.