A battery manufacturer supplies a range of car batteries to car manufacturers. The 40 Amp-hour battery is manufactured at two manufacturing plants with a stated mean time between charges of 8.3 days and a variance of 1.25 days. The company regularly selects an independent random sample from the two plants with results as shown in Table 6.2.

(a) For the given samples conduct an appropriate hypothesis test to test that the sample mean values are not different at the 5% level of significance.

(b) If the sample means are not significantly different test whether the population mean is 8.3 days (choose sample A to undertake the test).

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6.72 9.83 7.15 7.72 9.20 11.36 6.38 9.57 Table 6.2 Plant A 10.13 7.38 6.93 9.32 8.70 8.50 7.99 7.23 9.31 9.36 7.23 8.32 9.32 8.86 9.34 8.91 7.83 9.23 8.70 10.65 8.09 10.06 6.62 10.74 9.93 10.36 9.06 8.08 9.82 9.56 7.81 7.27 Plant B 8.10 7.81 7.58 8.35 6.51 7.98 6.62 8.14 6.27 9.69 8.01 7.78 8.33 8.94 9.82 9.45 8.54 8.51 9.54 9.08 7.01 7.06 9.26 10.26