Hypothesis Tests
211 questions· page 1 of 22
The amount of time, in minutes, spent by a customer on one visit to a certain shop is modelled by the random variable . In the past, the values of and were 10.5 and 3.8 respectively. The shop has recently moved to a new location, and the manager hopes that the new value of will be greater than 10.5. He takes a random sample of 10 customers and notes the time they each spend in the shop. He then calculates the sample mean for these 10 times.
Using a hypothesis test at the 5% significance level, the manager finds that there is sufficient evidence to conclude that the new value of is greater than 10.5.
Stating a necessary assumption, find the smallest possible value of .
Later, Birgitte carries out a similar test at the 5% significance level, using another 30 throws of the dice.
Calculate the probability of a Type I error.
Use a binomial distribution to find the largest value of that would provide sufficient evidence that the director's belief is correct.
In another month, the director carries out a similar test at the 4% significance level using the 35 job applicants from that month.
Explain the meaning of a Type I error in this context, and state the probability of a Type I error.
Given that the proportion of job applicants with first class degrees this year is actually 0.05, find the probability of a Type II error.
You may assume that the standard deviation of the battery life is 2.3 hours.
Show that the value leads to rejection of the null hypothesis at the 5% significance level.
It is given that the value leads to rejection of the null hypothesis at the % significance level.
Find the set of possible values of .
The mean mass of packets of Trueleaf tea is supposed to be 500 grams. An inspector wishes to test whether this value is correct. He weighs 60 randomly chosen packets and notes the mass, grams, of each packet. The results are summarised as follows.
Test, at the 5% significance level, whether the population mean mass is 500 grams.
Laxmi finds that exactly 2 households in her sample contain more than 4 people.
Explain why it is impossible for Laxmi to make a Type II error.
Stating a necessary assumption, test at the 2% significance level whether the mean weekly profit has decreased.
The mean weekly profit for another random sample of 35 weeks is found and a similar test is carried out at the 2% significance level.
State the probability of a Type I error.
Given that the mean weekly profit is now in fact $718, find the probability of a Type II error.
The mean mass of packets of Trueleaf tea is supposed to be 500 grams. An inspector wishes to test whether this value is correct. He weighs 60 randomly chosen packets and notes the mass, grams, of each packet. The results are summarised as follows.
Test, at the 5% significance level, whether the population mean mass is 500 grams.