Hypothesis testing Hypothesis tests Hypothesis

Transcript:Hypothesis testing Hypothesis tests Hypothesis:
Hypothesis testing Hypothesis tests Hypothesis testing KUS objectives BAT Test a hypothesis at a given significance level for one and two tailed tests Starter: WB 5 Cars entering a car park have to turn left or right. A survey is done of 20 cars. It is found that 15 went to the left. At the 5% significance level, does this mean car drivers have a preference for a particular direction? The evidence supports that we REJECT the hypothesis There is evidence to suggest that car drivers have a preference for turning left The probability that 15 or more turned left Binomial distribution n = 20 x = 15 The evidence supports that we do NOT reject the hypothesis There is no evidence to support the Doctors claim WB 7 Brad planted 25 seeds in his greenhouse. He has read in a gardening book that the probability of one of these seeds germinating is 0.25. Ten of Brad’s seeds germinated. He claimed that the gardening book had underestimated this probability. Test, at the 5% level of significance, Brad’s claim. State your hypotheses clearly. X = number of seeds germinating H0 : p = 0.25 H1 : p > 0.25 Accept H0 as there is insufficient evidence to support Brad’s claim Two tailed tests So far you have seen what are known as 1-tail tests – when H1 is that the parameter in question has either increased or decreased In a 2-tail test, H1 is simply that the parameter in question has changed When doing a 2-tail test, the significance level is shared equally between observations which are less than what was expected and more than what was expected. WB 8 Over a long period of time it has been found that in one long running Mexican restaurant the ratio on non vegetarian to vegetarian meals is 2:1 In Manuel’s Mexican restaurant in a random sample of 10 people ordering meals one ordered a vegetarian meal. Using a 5% level of significance, test whether the proportion of people in Manuel’s restaurant is different to that of the long running restaurant Binomial distribution n = 10 x = 1 Do NOT reject the hypothesis There is no evidence the ratio is different at Manuel’s WB 9 A manager tells their sales staff that they make a sale to 45% of customers entering their shop. The manager randomly selects 40 customers. Of these, 25