Final answer:
The question involves calculating a test statistic and seems drawn from a statistics context, likely requiring a two-sample t-test to compare the means of the thermostats from old and new suppliers. However, the specific test statistic cannot be determined without additional details such as the data's distribution or which test (z-test or t-test) is appropriate.
Step-by-step explanation:
The question provided appears to involve calculating a test statistic comparing two samples for a hypothesis test. This is a concept in statistics. Specifically, this might relate to a two-sample t-test if the population standard deviations are unknown, or a two-sample z-test if the standard deviations are known and the sample sizes are large enough. Since the sample sizes given are 19 and 21, which are not particularly large, and because standard deviations are provided rather than population variances, we would likely use a two-sample t-test here.
However, the question does not provide enough information to complete the calculation, as it would require knowing which test (z-test or t-test) to apply and whether the data follows a normal distribution. I cannot calculate the test statistic without this information. In any case, the calculation of a test statistic is essential for determining if the difference between two sample means is statistically significant.
To compute a test statistic for comparing two independent sample means, the general formula for a two-sample t-test is:
t = (x1 - x2) / sqrt((s1^2/n1) + (s2^2/n2))
Where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes for each sample, respectively. To perform a two-sample z-test, the formula is similar but would use the population standard deviations and z-distribution.