One-tailed hypothesis test (upper tail, H₁: p > p₀)

Carry out a complete one-tailed hypothesis test where the alternative hypothesis is that p has increased (H₁: p > p₀), state hypotheses, calculate probability, and draw conclusion.

52 questions · Standard +0.0

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OCR MEI AS Paper 2 2018 June Q9
7 marks Standard +0.3
In this question you must show detailed reasoning. Research showed that in May 2017 62% of adults over 65 years of age in the UK used a certain online social media platform. Later in 2017 it was believed that this proportion had increased. In December 2017 a random sample of 59 adults over 65 years of age in the UK was collected. It was found that 46 of the 59 adults used this online social media platform. Use a suitable hypothesis test to determine whether there is evidence at the 1% level to suggest that the proportion of adults over 65 in the UK who used this online social media platform had increased from May 2017 to December 2017. [7]
OCR MEI Paper 2 2022 June Q13
8 marks Moderate -0.3
Records from the 1950s showed that 35\% of human babies were born without wisdom teeth. It is believed that as part of the evolutionary process more babies are now born without wisdom teeth. In a random sample of 140 babies, collected in 2020, a researcher found that 61 were born without wisdom teeth. The researcher made the following statement. ``This shows that the percentage of babies born without wisdom teeth has increased from 35\%.''
  1. Explain whether this statement can be fully justified. [1]
  2. Conduct a hypothesis test at the 5\% level to determine whether there is any evidence to suggest that more than 35\% of babies are now born without wisdom teeth. [7]