Question

1. People claim that women say more words per day than men. Estimates claim that a woman uses roughly 20,000 words per day, while a man uses approximately 7,000. To investigate this, a researcher recorded conversations of male college students over a 5-day period. The results are as follows:

7220	13932	4727	10419
9258	9717	10728	5265
12215	9944	7979	12252
9307	9086	10780	3357

The researcher believes that many use more than 7,000 words per day.

1. State the problem in your own words.
2. Create a plan for testing the researcher’s claim. Be sure to state the null and alternate hypotheses.
3. Carry out the appropriate hypothesis test. Begin by finding the sample mean and standard deviation. Give the value of the t statistic and give the p-value (or an estimate).
4. Formulate the statistical conclusion in terms of the null hypothesis and a practical conclusion. You may compare the p-value to 0.05 to determine if the null hypothesis should be rejected. When the p-value is less than 0.05, we reject the null hypothesis. Otherwise, we fail to reject the null.

Answer 1

Answer:

(a). According to the Experts and peoples, Men are using less words in a conversation compared to women’s in daily conversation. Now to investigate this, the researcher record’s the 5 day conversations of male to check the words in a conversation 7000 or more than 7000?

(b). As per researcher, Here we need to check the the words in a conversation is more than 7000?

          So here we will state the hypothesis as,

             Null Hypothesis: The Male are using 7000 words per day conversation.

Alternative Hypothesis: The males are using more than 7000 words per day conversation.

(C). We can mention the hypothesis as,

                                          Null Hypothesis:H₀:µ=7000

                              Alternative Hypothesis:H_1:µ>7000

Here we used the R statistical tool for finding the mean ,Standard deviation, and t test statistic.

These commands are worked in R Programming only,

data<c(7220,13932,4727,10419,9258,9717,10728,5265,12215,9944,7979,12252,9307,9086,10780,335)

mean(data)

sd(data)

t.test(data,mu=7000)

Here im attaching the screenshot of the output:

Here Formulas as like:

Mean:

t test statistic:

(d).Conclusion:Here by our calaulation p value is 0.0092,its less than 0.05.So we reject null hypothesis. and we conclude that Mens are using more than 7000 words in a day.