| Tag | Value |
|---|---|
| file | Descriptive-statistics_vufsw-z-score-1176-en_vufsw-z-score-1176-en |
| name | vufsw-z-score-1176-en |
| section | descriptive statistics/score interpretation/z-score |
| type | schoice |
| solution | TRUE, FALSE, FALSE, FALSE, FALSE |
| Type | performing analysis |
| Program | calculator |
| Language | English |
| Level | statistical thinking |
Suppose that the current American president claims that the American population gives the current US president an average approval score of 7 (on a scale of 1 to 10).
A researcher has doubts about this claim and conducts a random survey among 121 American respondents. This sample shows that the average approval score is 6.5 (st.dev. = 1.8).
If we assume that the claim of the president is correct (i.e. that the average approval score in the population is 7), what is then then probability that we would find this sample statistic (this sample mean of 6.5)?
The probability is …
We first need to calculate the standard error: se = 0.1636.
Subsequently, we need to calculate the z-score for our sample statistic:
z = (6.5 - 7) / 0.1636 = -3.06
We can then find the P-value for this z-score (see Table A). The P-value of z-score -3.06 = 0.0011
Expressed in percentage: 0.0011 * 100% = 0.11%