Question

A researcher was tasked with determining whether the video display used by travel agents for booking airline reservations should be in color or in black and white. Market research has shown that travel agencies were primarily concerned with the speed at which reservations can be made. Therefore, the question was whether color displays allow travel agents to book reservations faster. Fifty subjects were tested with color displays (x-bar = 503 sec, s = 9.3 sec) and fifty subjects were tested with black and white displays (x-bar = 508.2 sec, s = 9.0 sec). Test if the reservations made on the color displays were significantly faster (less time) than those made on the black and white displays at a significance level of 0.05.

1.Write the null and alternative hypothesis.

2.α = Critical Value(s) =

3.Use technology to Calculate the test statistic

4.Draw a picture to show the rejection/non-rejection region

5.Use technology to find P-value

6.Would you reject the null hypothesis?

7.Write a conclusion

The agencies, however, are not concerned with statistical significance. The agencies would like to know if the difference in speed is of practical importance to them. Market research has shown that in order to justify the higher price of color displays, they must be faster by an average of at least 10 seconds per transaction.

6. Use technology to construct a 90% confidence interval for the difference in the means (colorminus black and white). the customer complaints?

7.Use the interval to explain to the agencies if they should or should not pay for color displays.Use complete sentences and proper grammar.

Answer 1

Solution :

1)

2)

3)

Following is the output of independent sample t test generated by excel:

The test statistics , t = -2.84

4)

5)

The p-value is 0.0027

6)

Since p-value is less than level of significance 0.05 so we reject the null hypothesis.

7)

There is evidence to conclude that reservations made on color displays were significantly faster than those made on black and white display.

6)

The 90% confidence interval is (-8.24, -2.16).

7)

Since confidence interval does not contain -10 so there is no evidence that color display is faster at least 10 second per transaction. So they should not pay for color display.

Let me know in the comment section if anything is not clear. I will reply ASAP!
If you liked the answer, please give a thumbs-up. This will be quite encouraging for me.Thank-you!