Chapter PVI, Problem 1RE

(a)

To determine

To explain is this difference significant.

Answer to Problem 1RE

The difference is not significant.

Explanation of Solution

It is given in the question that a study published found that babies born at different times of the year may develop the ability to crawl at different ages. Thus, the information is given as:

  $\begin{array}{l}{n}_1=32\\ {\overline{x}}_1=29.84\\ s_1=7.08\\ n_2=21\\ {\overline{x}}_2=33.64\\ s_2=6.91\end{array}$

Thus, for testing the hypothesis we will use the calculator $\text{TI}-89$ as, first we will go in the STAT TESTS menu, choose $4:2-$ SampTTest. Then you mustspecify if you are using data stored in two lists or if you will enterthe means, standard deviations, and sizes of both samples.You must also indicate whether to pool the variances (when indoubt, say no) and specify whether the test is to be two-tail,lower-tail, or upper-tail. So, now we will define the hypothesis as:

The null hypothesis needs to contain an equality and the alternative hypothesis states the opposite of the null hypothesis. Thus, we have,

  $\begin{array}{l}{H}_0:{\mu }_1={\mu }_2\\ H_a:{\mu }_1\ne {\mu }_2\end{array}$

Thus, by using the calculator $\text{TI}-89$ , the test statistics and the P-value is as:

  $\begin{array}{l}t=-1.939\\ 0.05<P<0.10\end{array}$

As we know that if the P-value is less than or equal to the significance level then the null hypothesis is rejected, so we have,

  $P>0.05\Rightarrow \text{Fail to Reject }{H}_0$

Thus, we conclude that since the null hypothesis is not rejected then the difference is not significant.

(b)

To determine

To explain is this difference significant.

Answer to Problem 1RE

The difference is not significant.

Explanation of Solution

It is given in the question that a study published found that babies born at different times of the year may develop the ability to crawl at different ages. Thus, the information is given as:

  $\begin{array}{l}{n}_1=26\\ {\overline{x}}_1=31.84\\ s_1=6.21\\ n_2=44\\ {\overline{x}}_2=33.35\\ s_2=7.29\end{array}$

Thus, for testing the hypothesis we will use the calculator $\text{TI}-89$ as, first we will go in the STAT TESTS menu, choose $4:2-$ SampTTest. Then you must specify if you are using data stored in two lists or if you will enter the means, standard deviations, and sizes of both samples. You must also indicate whether to pool the variances (when in doubt, say no) and specify whether the test is to be two-tail, lower-tail, or upper-tail. So, now we will define the hypothesis as:

The null hypothesis needs to contain an equality and the alternative hypothesis states the opposite of the null hypothesis. Thus, we have,

  $\begin{array}{l}{H}_0:{\mu }_1={\mu }_2\\ H_a:{\mu }_1\ne {\mu }_2\end{array}$

Thus, by using the calculator $\text{TI}-89$ , the test statistics and the P-value is as:

  $\begin{array}{l}t=-0.920\\ P>0.10\end{array}$

As we know that if the P-value is less than or equal to the significance level then the null hypothesis is rejected, so we have,

  $P>0.05\Rightarrow \text{Fail to Reject }{H}_0$

Thus, we conclude that since the null hypothesis is not rejected then the difference is not significant.

(c)

To determine

To explain are these results consistent with the researcher’s conjecture.

Answer to Problem 1RE

These results are not consistent with the researcher’s conjecture.

Explanation of Solution

It is given in the question that a study published found that babies born at different times of the year may develop the ability to crawl at different ages. Thus, these results are not consistent with the researcher’s conjecture because the results of the study were that babies born at different times of the year develop the ability to crawl at different ages while there were no significant differences in part (a) and part (b).