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STA1010 - Statistical methods for science - S2 2025

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A quality control check on the batch production of wooden skewers involves sampling and measuring the average length of the skewers per batch.

For Batch A, a random sample of 20 skewers were found to have an average length of 21.6 cm.

For Batch B, 10 random skewers  gave an average length of 20.4 cm.

The standard error in the difference was found to be 0.766 cm.

Calculate the 99% Confidence interval on the difference in length between the two batches (A-B).

Assume that the lengths are normally distributed, do not assume the population variances are equal, and use the conservative "by hand" estimate for the degrees of freedom (ie lesser n-1).

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When comparing two means, the situation most likely to lead to a result that is statistically significant but of little practical importance is

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It is known that for right-handed people, the dominant (right) hand tends to be stronger. For left-handed people who live in a world designed for right-handed people, the same may not be true. To test this, muscle strength was measured on the right and left hands of a random sample of 15 left-handed men and the difference (left - right) was found. The alternative hypothesis is one-sided (left hand stronger). The resulting t-statistic was 1.80.

This is an example of:
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A one-sample Z-test with a 2-tailed alternative hypothesis was carried out.

A z-statistic of 1.57 has been calculated for the sample mean.

Find the P-value, correct to three decimal places.

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A sample of n

= 9 men are asked. "What's the fastest you've ever driven a car?" The sample mean is 120 mph and the standard deviation is 30.

What is the value of the t-statistic for testing the null hypothesis that the population mean response is 100 mph?

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Classify the hypothesis test as lower-tailed, upper-tailed, or two-sided.

A health insurer has determined that the "reasonable and customary" fee for a certain medical procedure is $200.  They suspect that the average fee charged by one particular clinic for this procedure is higher than $200.  The insurer wants to perform a hypothesis test to determine whether their suspicion is correct.

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Construct the indicated confidence interval for the difference between the two population means. Assume that the assumptions and conditions for inference have been met.

A researcher was interested in comparing the number of hours of television watched each day by two-year-olds and three-year-olds. A random sample of 18 two-year-olds and 18 three-year-olds yielded the data.

 

2 year old

3 year old

average hours TV/day

1.25

1.44

standard deviation

0.81

0.78

sample size

18

18

Find a 95% confidence interval for the difference, μ2 - μ3, between the mean number of hours for two-year-olds and the mean number of hours for three-year-olds.

Use the conservative (lesser n-1) degrees of freedom.

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