Question

When the antihistamine Seldane was first introduced, it was heavily promoted because it supposedly did not cause drowsiness, unlike other antihistamines. During Clinical Testing, 9% of 800 Seldane users reported drowsiness, while 8% of 650 Placebo users reported drowsiness. Using the 5% level of significance, test the claim that the population proportion of Seldane users who experience drowsiness is less than or equal to the population proportion of placebo users who experience drowsiness.

1. Select the correct type of test    a. Two Tailed b. right tailed    c. left tailed

2. Find the critical values. If this is a one-tailed test, type "NONE" in the blank that does not apply.

Left Critical Value:

Right Critical value:

3. Find the Standardized Test Statistic. Round to 2 or 3 decimal places. Only value, no variable.

Standardized Test Statistic:

4. What is the P-value? Round to 4 decimal places

P-value:

5. Select the correct decision:

Reject ho

Fail to reject ho

Answer 1

1.
right tailed test

2)
This is right tailed test, for α = 0.05
Critical value of z is 1.64.
Hence reject H0 if z > 1.64

Left = None
right = 1.64

3)
p1cap = X1/N1 = 72/800 = 0.09
p1cap = X2/N2 = 52/650 = 0.08
pcap = (X1 + X2)/(N1 + N2) = (72+52)/(800+650) = 0.0855

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.09-0.08)/sqrt(0.0855*(1-0.0855)*(1/800 + 1/650))
z = 0.68

4)
P-value = 0.2483

5)
Fail to reject H0