Solve the below:
Q1. To reduce operating costs, First UP Bank wants to make sure that the loan department in its branches manage the number of courier packages sent out to appraisers etc. to 15 or less every week. The Bank examined the loan departments of 25 randomly chosen branches and the results show that an average of 14.2 packages with a standard deviation of 2.2 packages were sent during one week in late February. These numbers were fed into the Megastat Add-in in Excel and yield the following output:
Hypothesis Test: Mean vs. Hypothesized Value
15.000 hypothesized value
14.200 mean Packages
2.200 std. dev.
0.440 std. error
25 n
24 df
-1.82 t
.0408 p-value (one-tailed, lower)
At the 0.1 level of significance, is the true average number of packages less than 15? Please state the null and alternative hypothesis as well as the decision rule that you use to arrive at the conclusion.
Q2. A coin was flipped 80 times and came up tails 54 times. At the 0.05 level of significance, is the coin biased toward tails? Show your decision rule and calculations.