.6.1 Experience has shown that the diameter of a machined component is normally distributed, with an average diameter (μ) of 165mm, and a standard deviation (σ) of 2.5mm. A sample of 77 components is randomly selected. Q.6.1.1 Determine the standard error for this sample. Q.6.1.2 What is the probability that the mean diameter of the components in the sample will lie between 164.25mm and 164.75mm? Interpret your answer.
Q.6.1
Experience has shown that the diameter of a machined component is
Q.6.1.1
Determine the standard error for this sample.
Q.6.1.2
What is the probability that the mean diameter of the components in the sample will lie between 164.25mm and 164.75mm? Interpret your answer.
Q.6.2
It has been found that 14% of customers of an online retail store wait longer than five days for their order to be delivered. We assume normal distribution, and randomly select 115 customers.
Q.6.2.1
Determine the standard error for this sample.
Q.6.2.2
What is the probability that, for the sample of 115 customers, the proportion who wait longer than five days for their order to be delivered is less than 13.75%? Interpret your answer.
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Question 7
Q.7.1
Explain the difference between a Type I error and a Type II error.
Q.7.2
Explain the connection between the significance level and a Type I error.
Question 8
Q.8.1
A large manufacturing company claims that more than 88% of its customers are fully satisfied with the company’s products. Test this claim at the 5% significance level, if a survey found that 360 out of a random sample of 400 of the company’s customers said that they were fully satisfied with the company’s products.
Q.8.2
The CEO of Global Investment Funds claims that, on average, clients leave their investment funds with the company for a period of at least 56 months.
Test this claim at the 10% significance level, if it was found that a sample of 29 clients left their investment funds with the company for an average period of 58.85 months, with a standard deviation of 3.75 months.
Q.8.3
A shop owner claims that on average, his shop has a daily turnover of R75 000. Test this claim at the 5% significance level, if the average daily turnover for a sample of 88 days was R71 500. Assume a population standard deviation of R4 450.
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