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STA1010 - Statistical methods for science - S2 2025
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In the survey of a random sample of students at a university, two questions were "How many hours per week do you usually study?" and "Have you smoked marijuana in the past six months?" An analysis of the results produced the following results:
A research question of interest is whether students who have smoked marijuana (Yes group) in the past 6 months study fewer hours on average per week than those who have not (No group).
A survey of a random sample of students at a university was taken on these two issues, which found the mean hours of study for the following 2 groups:
Sample size, n | mean hours of study | Standard deviation, | |
Yes, Used marijuana | 49 | 12.41 | 6.95 |
No use of marijuana | 150 | 15.53 | 8.79 |
Difference = mu (Yes) - mu (No )Calculate the value for the t-statistic for the difference between the two groups.
State your answer to three (3) decimal places only.
In carrying out a two independent sample t-test for means, I have a choice of selecting "pooled" or "not pooled". If I select the "pooled" option, then I am assuming
In testing an hypothesis H0:µ = 10 against HA:µ <10, a one-sample t-test for the mean is to be used.
A simple random sample of 15 observations gives a mean of 9.9 and standard deviation of 0.25.
Calculate the standardized score (test statistic) for this sample, correct to two (2) decimal places.
A one-sample Z-test with a 2-tailed alternative hypothesis was carried out.
A z-statistic of -1.95 has been calculated for the sample mean.Find the P-value, correct to three decimal places.
In carrying out a paired two sample t-test for means, with H0:µ = 0 and HA:µ > 0 the 10 pairs of data yielded a sample mean difference of 1.23 and a standard deviation of 2.35 for this difference.
Find the test statistic, correct to two decimal places.
A manufacturer claims that the mean amount of juice in its 500 mL bottles is 503 mL. A consumer advocacy group wants to perform a hypothesis test to determine whether the mean amount is actually less than this.
Classify the hypothesis test as lower-tailed, upper-tailed, or two-sided.
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 90% 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).