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STA1010 - Statistical methods for science - S2 2025
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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.
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.
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.
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 researcher wants to prove that there is a difference in the average age of onset of a certain disease for men and women who get the disease.
A random sample of 30 women with the disease showed an average age of onset of 83 years, with a sample standard deviation of 11 years. A random sample of 20 men with the disease showed an average age of onset of 77 years, with a sample standard deviation of 4 years.
Assume that ages at onset of this disease are normally distributed for each gender, and that they are independent of each otherWhat is the value of the appropriate test statistic for (F) -(M)?