97) If the average of 3a and 4b is less than 50 and a is twice b, what
1 answer:
The average of and
satisfies
Then
, so if
must be an integer, then the largest integer value it can take on is 19 if
can be a rational number (in which case
) or 18 if
must also be an integer.
Given that none of the provided answer choices lists 18 or 19, I'd bet there's a typo and you're supposed to find the maximum integer value of , in which case the answer would be B as the largest integer value would be 9.
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Answer:
a)
b) We are uncertain
c) It will change significantly
Step-by-step explanation:
a) Since the variances are unknown, we use the t-test with 95% confidence interval, that is the significance level = 1-0.05 = 0.025.
Since we assume that the variances are equal, we use the pooled variance given as
,
where .
The mean difference .
The confidence interval is
b) With 95% confidence, we can say that it is possible that the gaskets from shift 2 are, on average, wider than the gaskets from shift 1, because the mean difference extends to the negative interval or that the gaskets from shift 1 are wider, because the confidence interval extends to the positive interval.
c) Increasing the sample sizes results in a smaller margin of error, which gives us a narrower confidence interval, thus giving us a good idea of what the true mean difference is.