Hypothesis Testing (I)

Question 1: Null and Alternative Hypothesis

Police are attempting to estimate whether or not motorists are traveling at more than the posted limit of 40km per hour in a certain school zone on average. Which of the following represents the correct set of hypotheses?

a. H_o:       = 40

H₁:       > 40

b. H_o:      m = 40

H₁:      m < 40

c. H_o:      m = 40

H₁:      m ¹ 40

d. H_o:      m = 40

H₁:      m > 40

e. H_o:       = 40

H₁:       < 40

Question 2: One or Two Tail?

For each of the following situations state whether or not the test is a one or a two-tail test; if it's one-tail, determine whether it is upper or lower tail. And state the hypotheses.

(a) A manufacturer of steel wire needs to test whether or not the wire being produced has an average diameter of 4mm.

(b) Past record shows the average part-time work of QUT students a decade ago is 15 hours per week. The career counsellor wishes to find out if QUT students today have more part-time work than a decade ago.

(c) Water quality experts for the forestry service would like to test whether the average phosphorous content has fallen below 15 parts per billion (ppb).

Question 3: ATM Withdrawals

ATMs must be stocked with enough cash to satisfy customers making withdrawals over an entire weekend. But if too much cash is kept unnecessarily in the ATMs, the bank is forgoing the opportunity of investing the money and earning interest. Suppose that at a particular branch, past record showed that the population mean amount of money withdrawn from the ATM per customer transaction over the weekend was $160 with a population standard deviation of $30. The bank manager wants to monitor the customers' withdrawals to see if the true mean ATM withdrawal is different from $160.

(a) If a random sample of 36 customer transactions indicates that the sample mean withdrawal amount is $172, is there evidence to believe that the true population mean withdrawal amount is different from $160, using the critical value approach? (Use a 0.05 level of significance)

(b) Calculate the p-value and interpret its meaning.

(c) What is your answer in (a) if the population standard deviation is $60 (use α = 0.05)?

 Question 4: Bowling Discount Voucher

The manager of AMF Bowling in Macgregor wants to test to see if a new promotion campaign using discount vouchers delivered to mailboxes of households in nearly suburbs has increased the number of patrons. Prior to the promotion the business was averaging 123 customers per day with a standard deviation of 5.6 customers. In the 16 days following the promotion the below customer numbers were recorded:

116

120

117

139

140

135

128

139

128

127

112

119

130

125

125

116

Test using a 5% level of significance using:

(a) the critical value approach, and

(b) the p-value approach.