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SCI1020 - Introduction to Statistical Reasoning - S1 2025

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The amount of time customers at a “Quick-Change” motor oil store spend waiting for their cars to be serviced has the Normal distribution with mean \mu\mu and standard deviation \sigma\sigma = 4 minutes. It is company policy that the customer wait time should be 20 minutes (or less). The manager of a particular store selects a random sample of 150 customer wait times and observes a mean wait time of 21 minutes.

A 99% confidence interval for the population mean wait time based on this sample was calculated to be (20.16, 21.84) minutes.

If the manager had decided to have more precision in making inference on the population mean \mu\mu, which of the following steps can the manager take to achieve the goal? 

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The amount of time customers at a “Quick-Change” motor oil store spend waiting for their cars to be serviced has the Normal distribution with mean \mu\mu and standard deviation \sigma\sigma = 4 minutes. It is company policy that the customer wait time should be 20 minutes (or less). The manager of a particular store selects a random sample of 150 customer wait times and observes a mean wait time of 21 minutes.

A 99% confidence interval for the population mean wait time μ based on this sample was calculated to be (20.16, 21.84) minutes.

If the manager had decided to construct a 90% confidence interval (instead of a 99% confidence interval) using the same sample wait times, the margin of error would

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The amount of time customers at a “Quick-Change” motor oil store spend waiting for their cars to be serviced has the Normal distribution with mean μ and standard deviation σ = 4 minutes. It is company policy that the customer wait time should be 20 minutes (or less). The manager of a particular store selects a random sample of 150 customer wait times and observes a mean wait time of 21 minutes.

If the manager had selected more customers for the sample, the margin of error in a 95% confidence interval using this data would

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The scores of a certain population on the Wechsler Intelligence Scale for Children (WISC) are thought to be Normally distributed with mean μ and standard deviation σ = 10. A simple random sample of 30 children from this population is taken and each is given the WISC. The mean of the 30 scores is 104.32.

Suppose a histogram of the 30 WISC scores is the following.

                 
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Based on this histogram, we would conclude that any confidence interval constructed from this sample

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The critical value, z*, used for constructing a 96% confidence interval for population mean \mu\mu is:

[read from the appropriate statistical table in the textbook]

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A bottling plant produces one-litre bottles of soda. The actual distribution of volumes of soda dispensed to bottles is Normal, with mean μ and standard deviation σ = 0.05 litre. We randomly select six (6) bottles and measure the volume of soda in each. The results of these six measurements (all in litre units) are

1.05,  1.04,  1.01,  1.06,  0.94,  0.99

Based on these data, a 90% confidence interval for μ is

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The population of the scores of all high school seniors that took a mathematics test last year followed a Normal distribution, with mean \mu\mu (unknown) and standard deviation \sigma\sigma = 100.  A simple random sample of 500 high school seniors that took the same test this year, had a sample mean of 512.

A 95% confidence interval for \mu\mu would be

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Crop researchers plant 100 plots with a new variety of corn. The average yield for these plots is

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= 130 bushels per acre. Assume that the yield per acre for the new variety of corn follows a normal distribution with unknown mean µ and standard deviation σ = 20 bushels per acre. A 90% confidence interval for µ is:

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A 99% confidence interval for the average weight μ of a population is computed from a random sample and found to be 4 to 8. We may conclude that

Select all correct answers: 

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A researcher selects a random sample. A 90% confidence interval for a population mean \mu\mu has

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