1. A sample of 30 sales records from a convenience store has mean R142. It is known that the standard deviation of sales receipts in this store is R34. Use these values to test whether or not the mean sale value at the convenience store is different from R148, at the 5% level of significance. Test the hypothesis and establish the p-value.
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
1. A sample of 30 sales records from a convenience store has mean R142. It is known that the standard deviation of sales receipts in this store is R34. Use these values to test whether or not the
2. An amateur long-distance runner knows his time taken to complete a 10km race has a standard deviation of 1 minute 51 seconds. The runner claims that his long-standing average is 42 minutes. If, for his last 15 races, he averaged 41 minutes 5 seconds, is this evidence that his mean time has improved? Test the claim at the 4% level of significance. What is the p-value for the test?
3. A pharmaceutical company wants to test the effectiveness of a new drug for a particular infectious disease. In a sample of patients with the disease, 24 were randomly assigned to receive the new drug, while the remaining 16 patients
were given a placebo. The length of time the infectious disease lasted was
recorded by a doctor for each patient. The sample mean for the group taking the new drug was found to be 6.5 days and for the control group (taking the placebo) the mean was 7.125 days. The (population) standard deviation of recovery times for people with the infectious disease is known to be 1.2 days. Test the claim that the drug reduces the time that an infectious disease lasts, at the 5% significance level. What is the p-value for this test? What assumptions do you need to make for this test to be valid?
4. Find (i) 95% and (ii) 90% confidence intervals for the difference in recovery times between the two treatment groups in question 3. You may assume the recovery times are
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