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Dr. Z thinks his class performed better on a recent exam than Mr. X's class. The scores of students in each class are displayed in the following table:
Dr. Z decides to conduct a t-test at the 10% significance level.
- [1]
Write down the null and alternative hypotheses for this test.
- [5]
Determine with justification the conclusion of this test.
- [2]
State the two assumptions Dr. Z makes in using a t-test.
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A toy company advertises that the types of mini-figures found in its cereal packets occur in the following long-run proportions:
A random sample of 160 packets is opened, giving the observed frequencies:
- [2]
State the null hypothesis H0 and the alternative hypothesis H1 for a χ2 goodness-of-fit test on the data.
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Copy the table below and complete the expected-frequency row, correct to the nearest integer.
Determine
- [1]
the value of the χ2 test statistic.
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the p-value of the test.
- [2]
At the 5% significance level, state with a reason whether the company’s claim should be rejected.