GATE Statistics, Experimental Design & Chemometrics for Food Science: practice questions

1 · Descriptive statistics and probability distributions: binomial, Poisson and normal · medium

Four replicate determinations of sugar content gave 8, 10, 12 and 10 g per 100 g. What is the sample standard deviation (n − 1 denominator)?

1. 1.41 g per 100 g
2. 2.67 g per 100 g
3. 1.63 g per 100 g
4. 2.00 g per 100 g

2 · Descriptive statistics and probability distributions: binomial, Poisson and normal · easy

Nine replicate fat determinations have a standard deviation of 1.2 g per 100 g. What is the standard error of the mean?

1. 0.40 g per 100 g
2. 0.13 g per 100 g
3. 3.60 g per 100 g
4. 1.20 g per 100 g

3 · Descriptive statistics and probability distributions: binomial, Poisson and normal · easy

Why are aerobic plate counts usually converted to log10 values before means are calculated and tests are run?

1. Log values are required by law for every microbiological result reported by a food laboratory worldwide
2. Taking logs removes the dilution factor, so the count no longer depends on the volume that was plated
3. Counts are right-skewed and close to log-normal, so logs give near-symmetric data with steadier variance
4. Counts are left-skewed with a long lower tail, and logs stretch that tail so the outliers become visible

4 · Sampling distributions, confidence intervals and hypothesis tests: z, t, chi-square and F · easy

A quality manager rejects a batch that in fact meets specification, because a test was significant by chance. Which error is this?

1. Type II error
2. Sampling bias
3. Measurement drift
4. Type I error

5 · Correlation and linear and multiple regression · easy

A fitted shelf-life model gives colour score y = 0.5 + 0.2x, where x is storage weeks. What colour score does it predict at 12 weeks?

1. 2.4
2. 8.4
3. 3.4
4. 2.9

6 · Correlation and linear and multiple regression · easy

Across 20 biscuit recipes, hardness and sweetness are strongly correlated. Both rise with sugar content. What does this show?

1. Hardness causes sweetness, because a strong correlation demonstrates a direct causal effect
2. Sugar, a shared cause, explains the correlation; hardness does not cause sweetness
3. Sweetness causes hardness, because the sensory attribute must drive the instrumental one
4. The correlation is spurious and must be zero once a larger number of recipes is tested

7 · Correlation and linear and multiple regression · medium

Why is adjusted R² preferred to R² when comparing regression models with different numbers of predictors?

1. It is always larger than R², so it makes good models look better for publication purposes
2. It removes the need to check residual plots, because it already corrects for non-linearity
3. It penalises extra predictors, so adding a useless term does not raise it automatically
4. It measures prediction error on new samples, so no separate validation set is needed at all

8 · Correlation and linear and multiple regression · medium

Panel scores and an instrument reading rise together but along a curve, and two samples are extreme. Which correlation measure suits this relationship best?

1. Pearson's product-moment correlation
2. The coefficient of variation
3. Spearman's rank correlation
4. The covariance in original units

9 · Correlation and linear and multiple regression · hard

A calibration line gives r = 0.995, but the residuals form a clear U-shaped pattern against concentration. What should the analyst conclude?

1. The response is curved; high r does not prove linearity, so refit or narrow the range
2. The line is adequate, because any r above 0.99 confirms that the response is linear across the range
3. The residual pattern reflects random noise only, so more replicates at each level will remove it
4. The intercept must be forced through zero, which will straighten the residuals and fix the fit

10 · Correlation and linear and multiple regression · hard

Five samples have sugar levels x = 1, 2, 3, 4, 5 and sweetness scores y = 3, 5, 4, 7, 6. What is Pearson's r?

1. 0.64
2. 0.80
3. 0.89
4. 1.00