Question

HW 42. 3

You wish to test the following claim (HAHA) at a significance level of α=0.05α=0.05.

      Ho:p=0.65Ho:p=0.65
      HA:p<0.65HA:p<0.65

You obtain a sample of size n=344n=344 in which there are 195 successful observations. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an approximation for the binomial distribution.

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =

The p-value is...

• less than (or equal to) αα
• greater than αα

This test statistic leads to a decision to...

• reject the null
• accept the null
• fail to reject the null

As such, the final conclusion is that...

• There is sufficient evidence to warrant rejection of the claim that the population proportion is less than 0.65.
• There is not sufficient evidence to warrant rejection of the claim that the population proportion is less than 0.65.
• The sample data support the claim that the population proportion is less than 0.65.
• There is not sufficient sample evidence to support the claim that the population proportion is less than 0.65.

Answer 1

Ho: p = 0.65

Ha : p < 0.65

Level of Significane (l.o.s.) : α = 0.05

Test statistics : Single proportion Z-test

Decision Criteria : Reject Ho at 5% l.o.s. if | Zcal | > Ztab or p-value < 0.05 ,
where Ztab = Z(0.05) = 1.6449 (from Z tables)

Calculation : = 195/344 = 0.56686   0.57.
Zcal = =   = -3.110846

P(Z < -3.110846 ) = 0.000932. ............(from Z tables)

Conclusion : Since | Zcal | > Ztab and p-value < 0.05, we reject Ho at 5% l.o.s. and thus conclude that the sample data support the claim that the population proportion is less than 0.65.

Hope this answers your query!