Question

x=c(4,4,12,8,3,17,15)

mean(x)

[1] 9

t.test(x,mu=6) #[t(7)=1.92, p=.097]

   One Sample t-test

data: x

t = 1.3887, df = 6, p-value = 0.2143

alternative hypothesis: true mean is not equal to 6

95 percent confidence interval:

3.714066 14.285934

sample estimates:

mean of x

       9

> t.test(x,mu=6,alt='g') #note the p-value is half

   One Sample t-test

data: x

t = 1.3887, df = 6, p-value = 0.1071

alternative hypothesis: true mean is greater than 6

95 percent confidence interval:

4.802251      Inf

sample estimates:

mean of x

       9

What does u represent in one of the sample t-tests?

What does ‘g’ stand for in the second t-test?

What should u be set to given 2 (instead of 4)choices per item?

Answer 1

For the first one sample t test for two tailed;

Null hypothesis: There is no difference in means,

Alternate hypothesis: There is a significant difference in means,

From the result summary of t test,

The P-value = 0.2143 is greater than 0.05 at 5% significance level hence the null hypothesis can not be rejected at 5% significance level. Now we can state that there is no statistically significant difference in means at 5% significance level.

For the second one sample t test for one tailed;

Null hypothesis: There is no difference in means,

Alternate hypothesis: There is a significant difference in means,

From the result summary of t test,

The P-value = 0.1071 is greater than 0.05 at 5% significance level hence the null hypothesis can not be rejected at 5% significance level. Now we can state that there is not statistically significant greater mean at 5% significance level.

Each step for R code is explain below,

Data Array => x=c(4,4,12,8,3,17,15)

Mean of Data Array => mean(x)

Output for mean => [1] 9

One sample t test for two tailed (where 'x' is the data array and 'mu' is the hypothesized mean comparing with the mean of array 'x' =>

t.test(x,mu=6) #[t(7)=1.92, p=.097]

Output of One Sample t test =>

One Sample t-test

data: x

t = 1.3887, df = 6, p-value = 0.2143

alternative hypothesis: true mean is not equal to 6

95 percent confidence interval: 3.714066 14.285934

sample estimates:

mean of x

9

One sample t test for one tailed (where 'x' is the data array and 'mu' is the hypothesized mean comparing with the mean of array 'x' and alt='g' means the alternative hypothesis is greater than hypothesized mean 'mu' =>

   t.test(x,mu=6,alt='g')

Output => One Sample t-test

data: x

t = 1.3887, df = 6, p-value = 0.1071

alternative hypothesis: true mean is greater than 6

95 percent confidence interval: 4.802251      Inf

sample estimates:

mean of x

9