Question

1. You wish to test the following claim (HaHa) at a significance level of α=0.002α=0.002.

      Ho:p=0.52Ho:p=0.52
      Ha:p≠0.52Ha:p≠0.52

You obtain a sample of size n=151n=151 in which there are 85 successful observations.

Determine the test statistic formula for this test.

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 not equal to 0.52.
• There is not sufficient evidence to warrant rejection of the claim that the population proportion is not equal to 0.52.
• The sample data support the claim that the population proportion is not equal to 0.52.
• There is not sufficient sample evidence to support the claim that the population proportion is not equal to 0.52.

2. You wish to test the following claim (HaHa) at a significance level of α=0.005α=0.005.

      Ho:μ=51.9Ho:μ=51.9
      Ha:μ≠51.9Ha:μ≠51.9

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=4n=4 with mean M=74.5M=74.5 and a standard deviation of SD=14.6SD=14.6.

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 mean is not equal to 51.9.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 51.9.
• The sample data support the claim that the population mean is not equal to 51.9.
• There is not sufficient sample evidence to support the claim that the population mean is not equal to 51.9.

Answer 1

Solution :

1 ) Given that

This is the two tailed test .

The null and alternative hypothesis is

H0 : p =0.52

Ha : p 0.52

n = 151

x =85

= x / n = 85 / 151 =0.56

P0 = 0.52

1 - P0 =1 - 0.52 = 0.48

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

=0.56- 0.52 / [(0.52*0.48) / 151 ]

= 1.05

Test statistic = z = 1.05

P(z >1.05 ) = 1 - P(z < 1.05) = 1 -0.8531

P-value = 2 = 0.1469 =0.2938

= 0.002

P-value >

0.2938 > 0.002

Fail to reject the null hypothesis .

There is not sufficient sample evidence to support the claim that the population proportion is not equal to 0.52

2 ) Given that

= 51.9

M =74.5

S =14.6

n = 4

This is the two tailed test .

The null and alternative hypothesis is ,

H0 :    = 51.9

Ha :     51.9

Test statistic = t

= (M - ) / S / n

= (74.5-51.9) / /

= 3.096

Test statistic = t =  3.096

P-value =

= 0.005  

P-value >

3.096 > 0.005

Fail to reject the null hypothesis .

There is not sufficient sample evidence to support the claim that the population mean is not equal to 51.9.