Question

1. For this problem you will need a t-table. What is the t-value needed for the critical value for a one-tailed upper hypothesis test with a sample size = 40 and alpha =.05?

2. For this problem it would be helpful to have a standard normal table. What is the z-value needed for a confidence interval of a proportion with a sample size of 600 and alpha equal to .10?

3. For this problem you will need a t-table. What is the t-value needed for the critical value for a one-tailed lower hypothesis test with degrees of freedom = 30 and alpha =.01?

4. For this problem it would be helpful to have a standard normal table. What is the z-value needed for the critical value for a one-tailed upper hypothesis test of a proportion with a sample size of 365 and alpha equal to .10?

Answer 1

1.

Degree of freedom = n-1 = 40-1 = 39

So, critical t-value at 0.05 level of significance for 39 degree of freedom for one tailed test is 1.685 (From t-table). We can also get this value by using R software as,

qt(1-0.05,39)

1.684875

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2.

Given,

Critical z value at 0.10 level of significance for two tailed test is

In R,

qnorm(1-0.1/2)

1.645

For one tailed test, critical z value is 1.282

In R,

qnorm(1-0.1)

1.282

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3.

Degree of freedom = 30

Direction: Left tailed test

So, critical t-value at 0.01 level of significance for 30 degree of freedom for one tailed test is 2.457 (From t-table).

Since, its a left tailed test,

In R,

qt(1-0.01,30)

2.457

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4.

Given,

For one tailed test, critical z value is 1.282

In R,

qnorm(1-0.1)

1.282

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