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2 years ago

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A researcher wants to determine whether the number of minutes adults spend online per day is related to gender. A random sample

of 315 adults was selected and the results are shown below. Find the expected frequency for the cell E2,2 to determine if there is enough evidence to conclude that the number of minutes spent online per day is related to gender. Round to the nearest tenth if necessary. Gender| 0-30| 30-60| 60-90| 90+ Male| 23|35|76|46 Female|31|42|46|16

1 answer:

suter [353]2 years ago

6 0

Answer:

The expected frequency for the cell E2,2 is = 33

Step-by-step explanation:

The given data is

Gender | 0-30| 30-60| 60-90| 90+ Totals

Male | 23 | 35 | 76 | 46 180

<u> Female | 31 | 42 | 46 | 16 135 </u>

<u>Totals 54 77 122 62 315 </u>

<u />

The expected frequency for the cell E2,2 is :

Expected for the (30-60 box for females) = Total of (30-6)/ (total )* females

= ( 77/315)135= 33

Here p= 77/315 and n= 135

therefor X= pn = 33

χ²= (33-42)²/33= 2.455 ( for the single value of E2,2=33)

Expected for the (30-60 box for males) = Total of (30-6)/ (total )* males

= ( 77/315)180= 44

χ²= (44-42)²/44= 0.09

The critical region is χ² (0.05) 3 ≥ χ²= 11.34

Let the null and alternate hypothesis be

H0:the number of minutes spent online per day is not related to gender

against

Ha: the number of minutes spent online per day is related to gender

The single value of χ² for E2,2 = 2.45 is less than the critical value of 11.34.

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