Statistic: hypothesis testing (null hypothesis and alternative hypothesis)
Question 1:
According to research of a telephone company, an average time of phone call per household is 86 times in a month. There was a change in phone charge last month. According to most recent research on 100 households, an average time of phone call has decreased to 84 times a month, and its standard deviation is 12. Please verify whether it supports the statement The reason for the decrease in times of phone call is due to change in phone charge. Use level of significance 5% to test this hypothesis
Question 2:
There is a factory that manufactures tire. The distance covered for the tire this factory manufactures is 25,000 km. This time they invented a tire with longer durability. 30 samples were selected for research, and the average sample mean was 25,500 km. The sample standard deviation is 1,700 km. Please verify the statement The new version of tire has improved in durability using level of significance 5% to test this hypothesis.
In addition to this question, please answer what will happen if the significance level is changed to 1%. Also in order to reject the null hypothesis, please calculate what the greatest value of significance level should be (p value).
Question 3:
The percentage of supporter for B party who has voting rights in city A has been 32%. In 1994, there was political change in government and wants to find out whether there was change in percentage of supporter for the party. The research was performed on sample of 200 people and the supporter average mean for the B party was 37%. The sample standard deviation was 48%. Please verify if party B’s support rate has increased significantly.