Question

4. Hypothesis testing for the population proportion. This next problem focuses on using technology to perform a hypothesis test for the true proportion of students with no credit card debt. Prior studies seemed to indicate that the true proportion of students with no credit card debt was 10%; however, new data leads a researcher to claim that the true proportion of students with no credit card debt is different than 10%. You will test this claim. Use appropriate technology with a significance level α = 5%. Identify the best estimate for the population proportion. 12 out of 100 have no credit card debt.

Sample values:

8331
4596
3617
3123
4435
1182
3235
1781
3479
1552
0
1432
7111
1266
2971
0
1099
1145
4519
2666
2284
1205
0
4819
1366
1213
1411
4717
5982
1276
3802
7299
2161
2225
1651
3417
1804
1230
2392
1286
3499
1564
0
2694
4925
0
3734
3350
1229
1479
2905
3685
0
6089
0
2090
2202
5430
6449
1230
0
1722
3916
3924
5165
2934
1561
4697
1102
5651
4818
7090
6014
1640
2425
3056
2442
7012
4344
6178
1271
2417
1261
3688
0
2618
3513
8339
1464
3291
0
9037
3904
1198
7406
1208
0
7835
0
6192

Answer 1

We have to test the claim whether the true proportion of students with no credit card debt is 10% or different, i.e. different means either less than 10% or greater than 10%

So, it is a two tailed hypothesis.

For null hypothesis, we will assume that the true proportion is unchanged and equal to 10%

For alternate hypothesis, we will test that the true proportion is changed and not equal to 10%

We have to use z proportion test in this case because we have sample proportion and population proportion.

Formula for z test statistic is given as

where

setting these values, we get

this gives us

z = 0.67

Now, we have to find p value corresponding to this z value at 0.05 level of significance.

Using z distribution for z value = 0.67 for two tailed hypothesis test. (look 0.6 in left most column and 0.07 on top most row, pick the intersection of these column and row)

we get

p value = 0.5029

It is clear that p value is greater than 0.05 level of significance. So, result is significant.

we failed to reject the null hypothesis.

So, we can conclude that there is insufficient evidence to support the claim that true proportion of students with no credit card debt is different than 10%.